C ontents EBSi Q&A

Transcription

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2 C otets EBSi Q&A

3 S tructure EBSi EBSi VOD

4 0 f() a a f() a f() a f()=a af() a, a =a f() f()=c c a f()=c f() a a f() f() f()= af() a f() f() f()=- af() - a a a a a a a-0 a-0f() a f()=a a =a f() a aa a+0 a+0f() a f()=a a =a f() f()= f()=a a f()=a a-0 a+0 a a-0 a+0 3 f(), g(), h() f()=a, g()=b, a, b kf()=k f()=ka k a { f() g()}= f() g()=a b a f()g()= f() g()=ab a a a a f() f() a a = = 5 ( g()+0, b+0) a g() g() b a a f() g() f() g(), a b a a f() h() g() a=b a h()=a a - a a a a 4

5 +0 []=, a []=- -a = (-a) a+0 -a = (a-) a-0-0 a+0 a-0 0 a, b +0-0 [] +[]-6 =a [+] =b - a-b [] =f() --0 =f() f()+f(0)+ f() _ O _ 0 ( +a+ (>) f()={ 0 (=) 9- ++b (<) a, b f() a +b f()=, f(0)=, f()=- f()+f(0)+ f()=++(-) = 5

6 03 { - } =f() =f() O _ f()= 0 f(-)=0 -<a<ka f() a k ;0); 0 af() 0g() 0 f() ;0); a g() ;0); ;0); 'ƒ ;0); - +- ƒ+8-3 = = ( +)('ƒ+8+3) =_6= (-)( +)('ƒ+8+3)

7 05 f()=, g()=3+ - (gá f )()-( f Ág)() f() g() f() { f()-g()} g() (" +3--" -+) (3-)[{;[!;} 0 +{;[@;} 9 ++{;[(;} +: [º:] (" +3--" -+) = 4-55 " +3-+" -+ 4-;[@; = 55 Æ +;[#;-:; ;: +Æ -;[!;+:; ;: =;$;= 7

8 " 4 +-+" -+3 ;!; ;3@; ;4#; ;5$; ;6%; 4 a f() h() g() a f()= g()=a a a h()=a a f(), g() 08 - " f(), f()g() g() a f() g(), f() a a g() a g() f(g()) a a a a 09 ( +a) +!% +a=a - f()=, g()= 0 f()=0, 0 f()g()=0 0 g() f() a g()=a, a =b ab g() a f() f()= a [g() ] g() = g() =ab f()=, g()= g()=0 0 a 0 f(g())= f()= 0 a f() g() 0 8

9 0 f(), g(), f()=5, {f()-g()}= {3f()+g()} a 5 0;0); f() a+log f() a+log 3 (-)f() =6a f() f() f() =0, =5 0 f()= -, f() , ;0); f(), g() f()= f()+g() =3, f()+g() f()-g() f()-g() =;pq; p+q f()+3g(),p,q f() =0 f() f() 0 = f()=f(0)=0 f()=a +b,a,b 0 f() a +b 0 = 0 = 0 (a+b)=b b=5 f()=a +5 a +5= =- 4a-0=-, 4a=8 a= f()= +5 f()=7 9

10 3 4 -!% -++a 33=b a, b +, a+b -: 4 : -;4%; 0 ;4%; : 4 : f(), g(), 0 f() g() =, =3 - f(-)+g(-) ;!; 0 6 g(f()) f()=t a+0 a+0, f() b+0 a+0 g(f())= g(t) a+0, f() b-0 a+0 g(f())= g(t) a+0, f()=b a-0 t b+0 t b-0 a+0 g(f())= g(b) g(f()) { 0 4} =f() ;!; 3 =f() O f(f())+ +0 f(f()) 5 f() f() f() f(0)=3 f()f(-) =-8 (-), f() f()=t +0, t f(f())= f(t)=3 f( f())=f(3)= f(f())+ f(f())=3+=5 +0 t

11 6 f()=, g()= -+3 f(g())+ g(f()) =f(), =g() =f() O _ =»() O _ f(), g() f(-)=f(+), g(+)=g(-) f()g()=0 f(g())= g(f()) f(g(+4))= g(f(+4)) { 0 4} =f() 3 O =f() f(f())+f(f())+ 3+0 f(f())

12 7 =f() (t, f(t)) t 9 a P(, ) a = - f(a), f(a) a ;3!; =+ A(-, 0) P(t, t+)p =+ AQ Q t AP =+ Q P 0 = P(t, t ) OP l A (OA -OP ) t O t>0 = A P A O O l ;#; ;%; 3 0 ;!; ;#; 5 PQ =-(-t)+t+ =-+t+ Q(0, t+) AP =(t+) +(t+) =t +4t+ AQ = +(t+) =4t +4t+ AQ 4t +4t+ t = t = AP t +4t+ l =;!; +4, =a + 4 l a =;!; +4 P{t, ;!;t +4} a ;!; (t +t+8) {a>0, a+;!;} =;!; `+4 =a `+:; ;: a ` P O l

13 0 a, b(a<b) { a b}, { a<<b}, { a <b}, { a< b} a, b, (a, b), a, b), (a, b, a, b (a, b), a, b) (a, b a { a}, { <a}, { æa}, { >a} (-, a, (-, a), a, ), (a, ) (-, ) f() =a f(a) f(a) f() a a f()=f(a), f() =a =f() =a f() =a f() (a, b) f()(a, b) f() (a, b) f()=f(a), f()=f(b), f(a), f(b) a+0 b-0 f() a, b 3 f(), g() f() f() g() cf() cf()g() g()+0 g() =f()(-, ) f() = 55555, f(), g() g()=0 g() 4 f() a, b f() 5 f() a, b f(a)+f(b), f(a)f(b) k f(c)=k c(a, b) f() a, b f(a)f(b)<0 f()=0(a, b) 3

14 f() =a f() =a =a f(a) f() a a f()=f(a) HjK f()= f()=f(a) a+0 a a (æ) f()= g - +a+4 (<) a ( +a-0 (+) f()= { - ª b (=) a, ba+b f() = f() = f()=f() +a-0 - =b a-0=0 a= (+5)(-) = =7 - - b=7 a+b= ( si ;[!;+4 (+0) f()= {!% +- ª a (=0) =0 a a, b, (!% + +a -b (+0) f()= { 9 ;4!; (=0) =0, a+b

15 =a =a a 04 +a (<0) f()= g, g()= (æ0) g( f()) =0 a -;#; -;!; 0 ;!; ;#; f()= -+a g() f(+) ( 0) g()= g f(-) (>0) ={g()} =0 a ={g()} =0 {g()} = {g()} ={ g(0)} -0 f() { g()} = { f(+)} ={ f()} =a -0 { g()} = { f(-)} ={ f(-)} =(+a) {g(0)} ={ f()} =a ={g()} =0 a =(+a) 4a+4=0 a=- 05 ( ( ) f()= { + (<<3) ª -4+6 (æ3) g()=( +a+b)f(), a, ba+b 5

16 06 =f(), =g() =f() =»() _ O _ O f()g() =- f(g()) =0 g( f() ) = 3 <, >, =, =-, < =0, > 3 =0 f()= -4+ag()= -b + 3 -b + h()=f()g() h() a, ba+b <, >, =, =- g() -b >, <b- >b+ =0 g()= -b =, =b- =b+ g(b-)=;#;, g(b+)=;#; -b <, b-<<b+ -b =0 g()= -b ;#; =»() O b_ b+ g() =b-, =b+ f()= -4+a h()=f()g() f(b-)=f(b+)=0 b-, b+ -4+a=0 b=4, b -=a b=, a=3 a+b=5 6

17 07 f()= a +a 3 =, + 4 f() = f() f()= =, = si a f()= 4 +, a 0<a p p p p 4 3 p ;#; p (0, ) f()= -log ;4!; ;3!; ;!; ;3@; ;4#; = -log f() -log =log ;5!; 0<< log ;5!; >0 f() log ;5!; log ;5!; = =;5!;, log ;5!; = ={;5!;}, f() 09 f()= (-) + +(-3) (-) +(-3) (-, k) k ;5!;+{;5!;} +{;5!;}3 += =;4!; ;5!; 34 -;5!;

18 0 {;5!;, 5} f()=[;[!;] f()=-[;{;], g()= -4 =f() =f() _ O 4 f()+k k f(g()) =0 { f()-}{g()+4} = ( +a (æ, +) f()= { ª b (=) = a, b a +b 8

19 5 a, b f() f()=0 (a, b) f(a) f(b) g( f())+;!;=-+;!;=-;!; g( f())+;!;=0, g( f())=-;!; - =f() =g() =f() O O =»() _ 3 log +-=0 (, ) (, 3) (3, 4) (4, 5) (5, 6) g(f())=- - g(f()) =0 g(f())=-;!; g( f())= g(t)= g( f())= g(t)=0 g( f())=0 g( f(0))=g()=- g( f())= g(t)=0 +0 g( f())= g(t)=0-0 - t -+0 t +0 t -0 t -+0 g( f()) =0 f(), g(), f() g( f()), 4 f() f(-)=, f()=- (-, ) f()+=0 f() -3 f(-) =0 si f()+cos f()=0 g( f())+;!;=0+;!;=;!;, 9

20 대단원마무리 Level a =- 3 a - a -- ;3$; ;3%; ;3&; ;3*; ;[!; {5++ } - -;#; -;!; 0 ;!; ;#; 03 f() f() f() f() =, =,a+0 a -a 3a -3a a -a f() f() {!$f()-!%f(-)}=3 -, f(0)

21 05 p p f() >0 +4+si ;5; f() +4+cos ;5;, {!$f()-+} g() ( g() \ (+0, +) (-) f()= \ 4 (=0) 9 0 (=), g(3) 07 += P(t, -t) + = AB A, B t +0 BP t> A B / `+ `= _/ O A / P _/ B +=

22 대단원마무리 Level- 0 f()- f( f())- f() =, a ++a -3a+3=0 f(a) f(a) a =f() -, { f()-}{ f()-} - 4 f() O =f() f( f()) =-

23 04,, O, A, B AOB=60, O B 0 ;3!; ;!; A 05 ABCD AB =, AD =CD =, BC =, -0 - A D C B 0 06 f(), f{ {;!;}k }=f() k= =f() f{ (-) k+ {;!;}k }=3 f{ (-) k+ {;!;}k }=f{;3!;} k= k= O ;3!; 3

24 03 =f() a b f() D f(b)-f(a) f(a+d)-f(a) = 3= 3, D=b-a D b-a D f() a b =f() P(a, f(a)), Q(b, f(b)) PQ f(b) f(a) O =f() Q D P D a b f() =a f '(a) D f(a+d)-f(a) f '(a)= = 3 D 0 D D 0 D f()-f(a) f(a+h)-f(a) f '(a)= 3= a -a h 0 h f() =a f '(a) =f() (a, f(a)) f(a+d) f(a) O a =f() D D a+d 3 =f() =a f '(a), =f() =a =f() =a =f() =a 4 =f() f '() D f' f '(), f '()= = D 0 D D 0 f(+d)-f() 3 D d d =f() ', f '(),, f() d d =f() f '() f() f '()=f() (, f()) 5 f(), g() =c c '=0 = '= - =cf() c '=cf '() =f() g() '=f '() g'() =f()g() '=f '()g()+f()g'() 4

25 f() =a =f() =a f '(a) f(a+h)-f(a) f()-f(a) f '(a)= = 3 h 0 h a -a 0 =f() f(-)-f(-)= - +3, f '(-) f() f '() 3 f() f()- 4 =3, - 3 ;&; 4 ;(; 5 f()- - =3 0 0, {f()-}=0 f()= f()- f()- = [ _ ] f()-f() = _ - + =f '()_;!;=3 f '()=6 f '() =;^;=3 f() 0 03 f(+)-3 f() =4, - f(+ah)-f() 4 =6 a h h 0 ;4!; ;!; ;4#; ;4%; f()g(), f '(a),a g(0)=g'(0)=4 f(a+h)-f(a)-g(h)+4 3=6 h 0 h 5

26 f() =a f() =a f(a+h)-f(a) f(a+h)-f(a) 3, 3 h +0 h h -0 h 04 h 0 f(+h)-f(-h) h h - -h = h 0 =0 h =0 =0 = = =+ f() f(+h)-f() =0 f()=f() h 0 3 h f(+h)-f() =0 h 0 3 h f(+h)-f(-h) 3 =0 h 0 h f()= -, f(+h)-f(-h) 3 =0 h 0 h h 0 =0 f '()=0 f() = = f()=f() h 0 f '()=0 h 0 = f(+h)-f() h f(+h)-f() h h 0 =0 f(+h)-f(-h) h f(+h)-f()-f(-h)+f() h 05 f(0)=0 f() g() ( f() (+0) g()= { ª 0 (=0) g() =0, =0 f() g() g() =;!; f '()+;!; f '() =f '()=0 f()= - h 0 f(+h)-f(-h) h = h 0 +h- - -h- h 6

27 3 f() f '(a) f '() =a f(a+h)-f(a) =f '(a) h 0 h 06 f()=;3!; -8+ f(3+h)-f(3) 3 h h f()= (a, b) 4,a +b =f() (a, b) f '(a) f()= f '()=4 - + (a, b) 4 f '(a)=4a -a +a=4 a -3a +3a-=0, (a-) =0 a=, b=f()=7 a +b = +7 = f()=- +4, g()= -3+5 f(+h)-g(-h) h 0 h ;!; ;#; ;%; 08 f()= [f{+;#;}-f {-;!;}] 7

28 4 f(), g() =f()g() =a h()=f()g() f '(), g'() h'()=f '()g()+f()g'() 0 f() g() g()=(3 -)f() g()=6, g'()=f'() f()=( +)(-) f '(-) f()=( +)(-) f '()=6 (-) +( +){(-)} f '()=(-){3 (-)+ +} f '()=(-)(5-3 +) f '(-)= (-) (-7)= =( +)( -+) (, ) f(), g() f(0)=, f '(0)=6 g(-)-4 4= - f()g()

29 5 ;0); f(a) f '(a) f() f()-b =c,a,b,c f(a)=b, a -a f '(a)=c f(h) f()= +a+b 3 =3 h 0 h, f '()+f(),a,b f(), f '() {f()} -f( ) =4 f() f '() 3=4 0 3 f() f()= +p+q 3 =-4 - f(a+h)-f(a-h) = h 0 h a,a,p,q ;0); f() a (, a+, a+0, ) { f()} -f( ) a -a =a(a-), f() a +3 0 =+3 =3 a(a-) 4 =4 a a=5 a+0 f()=5 +b +c+d f '()=5 +b+c f '() 5 +b+c = 0 = (5 +b+c)=c= b+c 5 +b = 0 0 = (5+b)=b=4 0 b= f '()=5 +4 f '()=5+4= f() f(3)+f'(3) f()- 3 =- +-3 f() =4-9

30 6 f(), g() f() (<a) h()= g =a, g() (æa) 5 +3+a (<0) f()= g +b+4 (æ0) =0, a, b a+b h() =a a-0 f()=g(a) h() =a h -0 f(a+h)-g(a) = h h +0 g(a+h)-g(a) h +a +b (æ) f()= g + (<) a, b,ab = -0 f()= f()=f() +=+a+b a+b= f()=+a+b=3 = h -0 h +0 = h +0 = h f(+h)-f() = h h -0 f(+h)-f() h h +4h = =4 h -0 h (+h) +a(+h) +b(+h)-3 h h +(3+a)h +(3+a+b)h h (+h) +-3 h =a+b+3 4=a+b+3 a+b= a=-, b=3 ab=-3 6 ( f()= { ª a (<-) +b+c (- <) - (æ) a, b, c, abc

31 7 =a f(a+h)-f(a) f()-f(a) f '(a)= 3 = h 0 h a -a 7 (+0) f()= g g()= f() (=0) g'(-)+g'(0)+g'() =f() f '()=-3, f( )-f(4) f '(4)=6, 3 - f()-f(-) =t -t 4 - f(t)-f(4) = t 4 =f '(4) t-4 =f() f(-)=f() -=s -s f()-f(-) f '(-)= = - -(-) f '(-)= f( )-f(4) -4 s f(s)-f() s- _(-) f '(-)=-f '()=-(-3)=3 f( )-f(4) = - f()-f(-) - s f(-s)-f(-) -s+ f( )-f(4) 3 (-) -4 f()-f(-) 3 -(-) f '(4) (-4) = f '(-) 6 (-4) = 3 = f() f '(0)=3, f(+)=f()+f()-6- f'{-;!;}

32 04 =f() (a, f(a)) -f(a)=f '(a)(-a) (a, b) =f(), =g() f(a)=g(a)=b, f'(a)=g'(a) =f() (a, f(a)) f '(a), m (t, f(t)), f '(t)=mt, (, ) (t, f(t)) -f(t)=f '(t)(-t)(, ) t,t-f(t)=f '(t)(-t) f() h f(a-h)<f(a)<f(a+h), f() =a f(a-h)>f(a)>f(a+h), f() =a f() =a, f '(a)>0 f() =a f '(a)<0 f() =a f(), < f( )<f( ) f() < f( )>f( ) f() f(), f '()>0 f() f '()<0 f() 3 f() =a =a, f() f() =a, f(a) f() f() =a, f(a), f() f '(a)=0 =a f '() (+) (-) =a f(a) (-) (+) =a f(a) 4 a, b f() (a, b) f() a, b f(a), f(b) 3

33 =f() (, ) =f '( )(- )+ (, ) f '( ) m m=f '(t) t (, ) (t, f(t)), -f(t)=f '(t)(-t)(, ) t =a+ba(0, ), B(, -), f()= -5+ a, b a-b (, 3) = - l l = - +a (, a) (0, ), a ;4!; ;!; 4 f()= - +a f '()=3 - f '()=3-= (, a) =-+a (0, ) =-+a a= =- +4 d,d 33

34 =f(), =g(), =f(), =g() =t f(t)=g(t) f '(t)=g'(t) 04 f()= +a, g()=b -4 = a, b a +b f()= -4+a, g()=- +-a,a f()= -4+a, g()=- +-a f '()=4-4, g'()=-+ =f() =g() =tf(t)=g(t), f '(t)=g'(t) f(t)=g(t) t -4t+a=-t +t-a t +t -6t=-a f '(t)=g'(t) 4t -4=-t+, 4t +t-6=0 t +t-3=0, (t-)(t +t+3)=0 t= t= +-6=-a a= f()= -4+a, g()=- +-a f()-g()= + -6+a h()= + -6+a h'()=4 +-6=(-)(4 +4+6) h() = f() g() =h() h(), h()=0 h()=+-6+a=0 O a= = -0-7 (-, -5) (a, a ) =, a f()= P(a, a ) g()= -4 Q(b, b -4) =g() a, b a-b

35 3 f() f() f '() f '()>0 f '()<0 f(), f() f()hjk f '()æ f()=a +b a, b (a, b) m m, < f( )<f( ) f()= f()= +a +a(-, ) a M, m, M-m f()= +a +a f '()=3 +a+a f()= +a +a - f '()=3 +a+aæ0 3 +a+a=0 D D 4 =a -6a 0 0 a 6 M-m=6-0=6 08 f()=;!; -4k + <0, >0 k a k b b-a ;9@; ;3!; ;9$; ;9%; ;3@; 35

36 4 f(), f(),,, f() =a f '(a)=0 =a f '() 0 f()=;3!; -a +(a+5)+ a f()=(-) (-4)+a 0, a f()=(-) (-4)+a f '()=(-)(-4)+(-) f '()=(-)(-8+-) f '()=3(-)(-3) f '()=0 = =3 f() 3 f '() f() f() =3 0 f(3)=(3-) (3-4)+a=0 a=4 4 f()= f '()=0 f()(-, 0) f() 09 f()= -3+a 3, a 36

37 5 f() f '() f() f() f '() f() f '() =f '() a O b f() m,, 0m+, <a f '()<0, >b f '()>0 f(), + f '() ( <) f '()= g - ( >), =f() =- f()=f(-) f(0)=0 f()>0 f '() f() f '() f() f '()=-<0, f '()=>0 f() =- f() f() f()>f(0) f(0)=0 f()>0 _ =f '() O _ O _ =f() 3 f() f '() =f '() f'(-)=f'()=0 f() =- f() =0 (0, ) f() =f '() O _ 37

38 6 a, b a, b f() a, b f(a), f(b) 5, 3 f()=a -3a +b 5, 4, a,a,b ;9!; ;6!; ;4!; ;3!; ;!; -, 0 f()= f()= f '()=3-6-9=3(-3)(+) f '()=0 =- =3 -, 0 f() f '() f() 6 8 f() =- f(-)=(-) -3(-) -9(-)+8= , f()= M, m M+m 4 -, a f()= , a, a>

39 O(0, 0), A(8, 0), B(8, 8), C(0, 8) OABC 8 PQRS P C B O A Q P R S =_ `+5 (-, -6) =- +5 PQRS OABC 8 f()= P(t, f(t)){0<t<;#;} Q, OPQ ;pq; p+q, O p q ;pq;, p+q,p q P (, - +5) OABC, PQRS S() S()=(- +5)=- +5 (0<<5) S'()=-3 +0=-3{-: 3º:} S'()=0 =0 =: 3º: 0<<5 S() (0) : 3º: (5) S'() = -6+9 (a, b) a, b a+b, 0<a<3 O = `_6+9 (a,`b) S() S() =: 3º: S() S{: 3º:}=-;:!)7):);+5 ;:!9):);=: º7º: p+q=7+500=

40 05 f()=a +b +c+d (a>0) f '()=0 a, b a O a b O a O f()=a +b +c +d+e (a>0) f '()=0 a a a a b c a b a a 3 f()=0 =f() f()=g() =f(),=g() >a f()æ0 >a f() (f() )æ0 >a f '()æ0 f(a)æ0 >a f()æg() h()=f()-g()h()æ0 4 Pt =f(t) D f(t+dt)-f(t) t t+dt P = 3 Dt Dt D d t Pv v= = =f '(t) Dt 0 Dt dt Dv dv t P v a a= = =v'(t) Dt 0 Dt dt 5 t l, S, V Dl dl = Dt 0 Dt dt DS ds 4= Dt 0 Dt dt DV 4= dv Dt 0 Dt dt 40

41 f(), f()=a +b(a, b,a+0) f() f(-)=-f() f() = 4, f(3) f()= -a +a+ a f()= -3+k- = k f(-)=-f() f()= -a f() =4 f() =f() = f() = O O a>0, f() -, f '()=3 -a=0 =Æ;3A; =-Æ;3A; f {Æ;3A; }=- 03 f() =a g()=f()-f(a) g() =a =g() >a g()>0 {Æ;3A; } 3 -a_æ;3a; =-, -;3@; aæ;3a; =-, a =7 a=3 f()= -3 f(3)=3-3_3=8 4

42 f(), 04 f() f(-)=f() f() = f() f() f '()=0a, b, c(a<b<c), f(a)f(b)f(c)<0 f() =b f()=0 f(a)>0 f()=0 b f(a)f(b)f(c)<0 =f() f(a)<0, f(b)<0, f(c)<0 a b c 05 - =f(), f() f(+)=f(-) f() = 7 f(a)<0, f(b)>0, f(c)>0 f(a)>0, f(b)>0, f(c)<0 a b c a b c f() =b f()=0 f(a)>0 f()=0 b 4

43 3 f()=0 f(), f()=0 _<0 HjK _=0 HjK _>0 HjK 06 = -3+4 =m m f()= a =g() g()=0 a 07 (log ) -6log +a=0 a =f() a g()= a g'()=6-6-=6(+)(-) g'()=0 =- = g() =-, = g()=0 g() _=0 g(-)_g()=0, (a-3)(a-30)=0 a=3 a=30 a f()=;4!; - +a+3 a 43

44 4 09 f() f '() f'(a)=0, f '(b)=0, f(a)=-, f(b)=: 8ª: =f '() a O b f()=0, f() -=0, f(0)>0, a>, f()= -3(a+) +6a-4a+ f()=0 b a, b f '()= a> f() = f()<0 f(b)=0 a b 6(+a)(+) > 6(+a)(+) < 6(-a)(-) > 6(-a)(-) < 6(-a)(-) > 0 ;3!; --+a=0 a a<;3!; ;3!;<a< <a<;3%; ;3%;<a< a> f()= -3(a+) +6a-4a+ f '()=6-6(a+)+6a= 6(-a)(-) f '()=0 =a = f() a f '() f() -a+ a> f() = f()=-a+<0 a> =f() =f() f(b)=0 a < b a b 44

45 5 f()æg() h()=f()-g() h() h() <0 +3 +a 0 a f()=5-0 +k, g()=5 + { 0 3} f()æg() k h()=f()-g()=5-0 +k-(5 +) h()=5-5 +k- 0<<3 h()=5-5 +k-æ0 (h()æ0 h'()=5-30=5(-)=0 =0 = 0<<3 h() (0) (3) h'() h() 0 3 h() = h() h()=k-æ0 kæ k > +4-k>0 k 3 (si ) +3a-æ0 a ;3!; ;3@; ;3$; ;3%; 45

46 6 t (t) v(t), a(t) P t =f(t), v(t)=f '(t), a(t)=v'(t) 4 Pt =t -3t +t(tæ0), 0 60Á 0.5 m m, t h(t) `m 60 h(t)=-5t (m),, -0 m -7 m -5 m - m -0 m hº ;!; 30 hº hº si 30Á=0.5=;!; 60 hº= tº h(tº)=-5tº = 5tº =0 tº= tº>0 t h'(t)=-0t h'()=-0 m 5 6 P t =t -9t +4t P P P, Q t f(t)=t -6t+5, g(t)=t -t -t P 6 Q P, Q 46

47 7 l, S, V t t l(t), S(t) V(t) Dl dl = Dt 0 Dt dt DS ds 4= 4 Dt 0 Dt dt DV 4= 4 dv Dt 0 Dt dt 9 cm, cm 0. cm, 0.3 cm, cm cm cm, apcm a 0 cm, 8cm mm, 4 mm, t V(t)0, cm 6p 64p 66p 68p 70p t (9+0.t) cm, (4+0.3t) cm S(t) S(t)=(9+0.t)(4+0.3t)=0.06t +3.5t+36 S'(t)=0.t t=4+0.3t t=50 S'(50)=0._50+3.5=9.5 cm 9 0 cm AB Pcm A B AB A B P AP, PB SPA S ap cm, a 47

48 대단원마무리 Level- 0 =f() f() - -+3, f '() =f() (a, f(a)) ;4#;p, h 0 f(a-h)-f(a) 3h -;#; -;3@; ;3@; ;#; 03 f() f()f '()= f() ;4%; ;#; ;4&; 04 f()= +a +b+c =f() a _ b O f'(a)=0, f'(b)=0, a<-, 0<b< a>0 b<0 3-4a+4b<0 48

49 05 f()= -a +3a+ a 06 f()= +;3$; +ag()= +4 f()>g() a a>;3%; a<;3*; a>: 3 : ;3%;<a<;3*; ;3*;<a<: 3 : 07 P, Qt f(t)=;3!; t +t -3t, g(t)=t + P Q P, Q 08 ABCB AB, BC 0.5, ABC A 3 ;!; B C 3 49

50 대단원마무리 Level- 0 f()= -3a +3(a+)+ =t g(t) g(t) t a f() f() f() 4 = 4 = 0 - f( f()) f()=0 f '()= 4 = - 03 f()g() (-)f()=(+)g() g() =3 - f()g() h() h() h'()

51 (-), Q() Q() Q'(0) f() ( f() (+) g()= { - 9 (=) g() O =»() f()=0 f '()= f '(0)= 06 f() g()={ f()}, (-c, c) g'()<0 f '(b)=f '(-b)=0, f '(0)=0, f(-a)=f(a)=0, 0<a<b<c 0<<a -a<<a -c<<-b b<<c 0<<a b<<c -b<<-a 0<<a b<<c =f() _c_b _a O a b c 5

52 06 F() f()f'()=f() F() f() : f()d f() f() f() f() F() f() F()+C : f()d=f()+c C F'()=f() : f()d=f()+c C d [: f()d]=f() d : «d= + +C =0 C + : k f()d=k: f()d k: { f() g()}d=: f()d : g()d =f() =f()[a, b] b-a b-a f( )D=:Ab f()d {D= =a+ k} :Ab f()df() a b a b :Ab f()d f()a b d d k= :A/ f(t)dt=f() [a, b] f() F'()=f() ab :Ab f()d=[f()]ba=f(b)-f(a) f(), g()abc O º ««a b = = :Aa f()d=0 :Ab f()d=-:ba f()d :Ab { f() g()} d=:ab f()d :Ab g()d :Ab k f()d=k:ab f()d k :Ab f()d=:ac f()d+:cb f()d (b-a)k f{a+ } b-a =:) b-a f(a+)d=:ab f()d k= 5

53 F'()=f() : f()d=f()+c C : «d= + +C + =03 C d [: f()d]=f() d f '() f() : f()d=f()+ - =f()(0, ) f() f()g() =f() P(t, f(t)) f() =(3t +4t+)+g(t) g() -3 -;!; 0 ;!; 3 f()g() f'()+g() f'()+g'()=3 + g()+f'()= -5 d : f()d=f()+f'()+3-4 d f()=f()+f'()+3-4 f'()=-3+4 f()=: f'()d f()=: (-3+4)d f()=-;#; +4+C C =f()(0 ) f(0)= C= f()=-;#; +4+ f()=3 03 f() f(+)=f()+f()+3(+)+ f'(0)=f() f'(0)=0 f() f() - 53

54 F'()=f() 04 :_! (-) d ;#; ;%; 3 ;&; :Ab f()d=[f()]ba=f(b)-f(a) :Ab {hf() kg()} d =h:ab f()d k:ab g()d hk :Aa f()d=0:ab f()d=-:ba f()d :Ab f()d=:ac f()d+:cb f()d 05 =f() f()f(0)=- :_! f()d=:) f()d=:_0! f()d a bo 3 c =f() f() :Ab f()d=:ac f()d+:cb f()d f() =f() :Ac f'() d a<b<c f'(a)=f'(b)=f'(c)=0 f(b)=3 f(a)+f(c)=3 :_! f()d=:_0! f()d+:) f()d :_! f()d=:) f()d=:_0! f()d :_! f()d=:) f()d=:_0! f()d=0 f()=a +b- a+0 :) f()d=:) (a +b-)d=[;3a; +;B; -]) :) f()d=;3a;+;b;-=0 06 f()=:) t- dt :) f()d ;3$; ;3%; :_0! f()d=:_0! (a +b-)d=[;3a; +;B; -]0_! :_0! f()d=;3a;-;b;-=0 ;3&; ;3*; a=3b=0 f()=3 - f()=-= 54

55 3 :Ab f()d=a 07 :@/ (t +at-)dt=5a :A/ f(t)dt=f(a) a -a :A a+h f(t)dt=f(a) h 0 h d :A/ f(t)dt=f() d d :A/ (-t)f(t)dt=:a/ f(t)dt d F'()=f() f() :!/ f(t)dt= -a +a f(3) a = -a+a=0 a= f()=3-4+ f(3)= f() g() g()=:!/ f'(t)f(t)dt g(-)=g() g() =6 - f()-g(0) 55

56 4 f()=f(+p) 09 f() -+ (- <0) f()=g -+ (0 <) f(+)=f() f(+)d b+c :Ab f()d=: f(-c)d a+c p f()=f(+p) ;!; ;3@; ;6%; ;6&; b+p b+p :Ab f()d=: f()d=: f()d a+p a+p f() - f()= -4 f()=f(+4) :! f()d 0 f() :_@ f()d= f(+)-f()= : f()d -: f()d : f()d -: f()d :_0@ f()d -3 -;%; : f()d 006 -;#; -;!; f() 4 f() f() =f() _4 _ O 4 :_@ f()d=3, :@4 f()d= f(+)=f(-) +4 :! f()d : f()d = = : f()d :! f()d=: f()d

57 5 =p f() f()=a(-) +b :_! f()d=, :)3 f()d=5 :) f()d ab f(-)=-f() :_aa f()d=0 f(-)=f() :_aa f()d=:)a f()d =p f(p-)=f(p+) p+a p+a : f()d=: f()d p-a p f«()={-;k+!a } :) f«'()d=- a a a a«a = k= f ()=3 (+) :) + f«()d=:) + f«()d 3 f() g()=(-a)(-b)f() f() :_! g()d=0 a +b a, b ;3@; ;3$; ;3%; a =S«f«()={-;K+!a } =(-S ) k= :) f«'()d=- f«()-f«(0)=- f«()=(-s«), f«()-f«(0)=- (+) (-S«) -S«=- S«= =, f ()=(-3) f ()= (+) f«()=[- ] + = :) + f«()d=:) + f«()d 57

58 6 pk p f{a+ } =:A a+p f()d k= 4 (+) +(+) +(+3) ++(+) =:)p f(a+)d =p:) f(a+p)d =f() =f() [0, ] f() g() k k- k [g{ }-g{ }] k= O 5 f()=3-4- g()= f{ k} k= g()+ - :) g()d :) f()d :) { f()-g()} d :) g()d :) f()d k k- k [g{ }-g{ }] k= 0 = [g{ }-g{ }]+ [g{ }-g{ }] - =++ [ g{ }-g{ }] 0 - =- [g{ }+g{ }+g{ }++g{ }]+g() - k =- g{ } k=0 - k = [- g{ }] k=0 =-:) g()d=:) f()d 58

59 6 {a«}, {b«} fi (a b ) a«+0 : 5 : : 5 : : 5 : 4 a =, b = =a«+ a«=:n + +3 (-)d, b«=: d + k= : 5 : 7 :Ab f()d= f( )D= f( )D k= {D= b-a - k=0 =a+kd} f()= +a+b (aæ0, b>0) [0, ] 0=º,,,, «, «= [, ] f( ) A k=,,, =f() A º ««0 = A«A = 7 + A +A«= 8k A k= A = f { }, A«= f() a A +A«= [ f { }+f()]= { + +b++a+b} 7 + A +A«= {+a+(+a+b) }= a=0 +a+b=7 b=3 f()= +3 8k A =8 [ k f{ k }] k= k= =8:) f()d=8:) ( +3)d =8[;4!; +;#; ]) =8{;4!;+;#;}=4 4 59

60 7 f()= + [0, ] 0=º ««= f( )+f( ) [ ] k= 3 ;4!; ;4#; ;4%; ;4&; ;4(; 8 f()=a (a>0) [0, ] º(=0),,,, «, «(=) (, f( )), (, f( )), (, f( )) A k=0,,, 3,, - f()=a (, f( )) A - O º=0 (, f( )) (, f( )) =««S()= A S()S(+)= k=0 a = 60

61 07 [a,b] =f() =a, =b S S=:Ab f() d O a =f() b [c,d] =g() =c, =d S d =»() S=:Cd g() d c O [a, b] =f() =g() =a, =b =f() =»() S S=:Ab f()-g() d O a b P t v(t) t=a P º t=b P º+:Ab v(t)dt t=a t=b P :Ab v(t)dt t=a t=b P :Ab v(t) dt t P (t)'(t)=v(t) :Ab v(t)dt=[(t)]ba=(b)-(a) (b)=(a)+:ab v(t)dt=º+:ab v(t)dt t=b P (b)=º+:ab v(t)dt t=a t=b P :Ab v(t)dt 6

62 0 ='ƒ+ ='ƒ+ = ;!; ;#; S=:Ab f() d S=:Cd g() d f()g() ;%;, ;3@;, {;3@;}, {;3@;} 3,, {;3@;} -, = = = 0 f()= + - =f( ) ;6%; ;6&; ;3$; ;#; ;3%; O ;3@; {;3@;}3 {;3@;} ;5 7; ; 9; ;5 7; ;5 7; ; 9; S S={-;3@;} +[;3@;-{;3@;} ] {;3@;} +[{;3@;} -{;3@;} 3 ] {;3@;} =f() =f'() =f() 0 =f() _ O, f'(-)=f'(0)=f'()=0 ;!5$; ;!5^; ;!5&; =f '() S=;3!;+;3!; {;3@;} 3 +;3!; {;3@;} 6 + ;3!; S= =;ª9; -{;3@;} 3 ;!5(; ;@5@; S-:) d=;ª9;-[;3!; ])=;ª9;-;3!;=;5 7; 6

63 S S=:Ab f()-g() d 04 = () ;3!; ;!; ;3@; ;3$; ;#; f()-g() = -+= ;9!; ;6!; ;9@; ; 8; ;3!; -+= -=(-)=0 0 f()= +4 f() f'() 05 : 4 : : 4 : : 4ª: : 4 : : 4 : = `_+ = O :) {-( -+)} d=:) (- +)d =[-;3!; +;!; ]) =-;3!;+;!; =;6!; 06 f()= +a +a a f()

64 3 [ab] =f() =a=b S [ab] f()æ0 S=:Ab f()d [ab] f() 0 07 = - = - =k k k> ;5^; ;4%; ;3$; ;#; ;3%; = `_ O =k S=-:Ab f()d f()= -5+4 S =f() f()= `_5+4 S S =f() S S O k =k (k>4) S S S S :)k f()d 3 ;&; 4 ;(; 5 S S S S S S S =S +S 08 f()=- =f() =m æ0 A =f() ==m =m =_ A B O = B m 0<m< ;!; ;3!; ;4!; ;5!; ;6!; :)k f()d=s -S +S :)k f()d=s :)k f()d=-:!4 f()d :)k f()d=-:!4 ( -5+4)d :)k f()d=-[;;3;; -;%; +4]4! :)k f()d=;(; 64

65 09 =f() =f() O a b 4 t=a t=b Pv(t) P :Ab v(t)dt F()=:)/ f(t)dt G()=:)/ f(t) dt [0b] =f() 0<a<bf(0)=f(a)=f(b)=0 [0b] =F() 3 [0b] =G()-F() P :Ab v(t) dt t v(t)(m/ ) t (0 t 0) v(t)=g 60-t (0 t 40) t=35 5 m 50 m 75 m 300 m 35 m t v(t) t (0 t 0) v(t)=g 60-t (0 t 40) t=35 :)3 5 v(t)dt=:) 0 35 tdt+: (60-t)dt 0 35 t :)3 5 v(t)dt=[ ])0 +[60t-t ] 0 :)3 5 v(t)dt=(00-0)+( ) :)3 5 v(t)dt=75(m) 65

66 0 P t v(t)=t -t 3 P ;3%; ;3$; 5 :Ab v(t)dt ;3@; ;3!; :Ab v(t) dt v(t) t t P t=0 t=6 v(t) v(t)=3t -8t+5 P P P t(0 t d) v(t) :)a v(t) dt=:ad v(t) dt v(t) 0<a<b<c<d P O a b c d t :)c v(t)dt=:cd v(t)dt :)b v(t)dt=:bd v(t) dt PQt v (t)=tvœ(t)=t -t PQ PQ PQ PQ =v(t) [0a][ac][cd] t ABC :)a v(t) dt=:ad v(t) dt A=B+C :)t v(t)dt>0 (0<t d) P :)c v(t)dt=:)a v(t)dt+:ac v(t)dt=a-b=c :)c v(t)dt=:cd v(t)dt =v(t) [ab][bc] DE :)b v(t)dt=a-d=(b+c)-d=(b-d)+c :)b v(t)dt=e+c=:bd v(t) dt 66

67 3 A() P t v(t) v(t) O t P v(0)=v()=v()=0 5 PQt(0 t b) v (t) vœ(t)v (t)vœ(t) v(t) v (t) vœ(t) ;3@; ;3$; ;3%; O a b t ;3&; ;3*; :)b {v (t)-vœ(t)} dt=0 0<a<b t=bpq t=apq 0<t<b PQ 4 v(t) P t(0 t c) v(t) O a b c t :)c v(t)dt=:ab v(t) dt P 3P t=c 0<a<b<c 67

68 대단원마무리 Level- 0 :_! (+)(+) d-:_! (+)(-) d : 3 : : 3 : 6 : 3º: : 3 : 0 f() :) { f'()+3 }d=f() f(0) :!/ (t+) 0 dt

69 04 f()=- + f {;K;};@;=:)a f() d k= a a> ;6&; ;5^; ;4%; ;3$; ;#; 05 (00)(0)()(0) ='ß= S S S S S +S ;8#; ;!; ;8%; O S = =/ S S ;4#; ;8&; 06 Pt v(t)=(t-)(t-a) P P a> ;3*; : 3º: 4 : 3 : : 3 : 69

70 대단원마무리 Level- 0 f() f()=0 f(-)=f() f() 0 f'()=0a:)a f'()d= E={34567} X (X)s(X)X E AB (A)-(B) + s(a)-s(b) A'B=E :) s(a) s(b) d=;3 0; :) (A) d+:) (B) d+:_0! (A;B) d> I«=:) «+ d I -I =;3!; 5 (-) k+ =I -I k= k- I«+I«= - 70

71 04 f() = =0 =f() 3:) f()d O 05 v(t) PQt(0 t b) v (t)vœ(t) v P (t) vœ(a)=0:)b {v (t)-vœ(t)} dt=:)b vœ(t) dt PQ t=b O v Q (t) a b t Pt=b :)a vœ(t) dt PQ P :)a vœ(t) dt t=bpq Pt=b 06 AOB PO A B 3 P OA AB A B PO A P O P A ;!; ;#; ;%; 7

72 08 r r r +r-c r r! P r = 0 r (-r)! r! C r = P r = 0 r r! (-r)!r! (a+b) = C 0 a + C a - b+ C a - b ++ C r a -r b r ++ C b (a+b) = «C a«b «C a«b C 0, C,, C «C (ær) C 0 + C + C ++ C r ++ C = C 0 - C + C - C 3 ++(-) r C r ++(-) C =0 C 0 + C + C 4 += - C + C 3 + C 5 += - r=0 (+) (+) = C 0 + C + C ++ C = C 0 + C + C ++ C r ++ C = =- C 0 - C + C - C 3 ++(-) r C r ++(-) C =0 + ( C 0 + C + C 4 +)= C 0 + C + C 4 += - - ( C + C 3 + C 5 +)= C + C 3 + C 5 += - 7

73 r +r- C r C 5 = 7 C 5 = 7 C 7_6 3+5-C 5 = = A, B, C,, A 4 A

74 + ++ =r r (,,, ) +r- C r f:x Y X, Y (X)=r, (Y)= a<xb<x a<b f(a) f(b) f +r- C r 05 X={,, 3, 4, 5} X X f X i, j i<j f(i)<f(j) X i, j i<j f(i) f(j) z=7,, z (,, z),, z (,, z) C 7 = 9 C 7 = 9 C 9_8 3+5-C 5 = = X={,, 3, 4} Y={5, 6, 7, 8} f f(3) X i, j i<j f(i) f(j) z=9,, z (,, z)

75 3 (a+b) = C r a -r b r r= (+ ) (+a) 80 fi a (+a) C a 7-r C _a = 80 35a =80 a =8 a= 7_6_5_4 4_3 fi C _a = C _4=_4=84 _a =35a d (+a)fi d : (+a)fi d a {-:; ;:}

76 4 (a+b) m +(a+b) (a+b) m (a+b) (a+b) m (c+d) (a+b) m (c+d) 0 (-)(+) k- k= (-) (-) (-) (-) (-) (-) Cº (-) _ C (-) =6 (-) (-) C (-) _ C (-) =48 (-) (-) C (-) _ Cº (-) = =0 0 (- ) (++ ) (- ) (++ ) =(+) (- ) (+) (- ) (+) (- ) (+) (- ), + f() ab f(a+b) (-) +(+)fi

77 5 (+) (+) =«Cº+«C +«C ++«C««Cº+«C +«C ++«C ++«C«= «Cº-«C +«C -«C ++(-) r «C ++(-) «C«=0 «Cº+«C +«C += - «C +«C +«C += - 4 A A 04 A f()= ( k C + k C + k C ++ k C k- ) k= f(5) kc + k C + k C ++ k C k- = k- f(5)= k- = ( 4 k- ) f(5)= 5 k= (4fi -) 4-5 k= 03 f(5)= 3 = 34= (-), (+) k (k=0,,,, ) a, b a 3= k=0 b a 35 = k=0 b b (a +b ) 35 = - k=0 a 3 7 C r= fi fl

78 09 S A P(A) P(A)= (A) (S) A r P(A) P(A)= r«s A 0 P(A) P(S)= P(u)=0 A, B P(A'B)=P(A)+P(B)-P(A;B) A, B A;B=u P(A'B)=P(A)+P(B) A AÇ P(A)=-P(AÇ ) 3 A, B A B P(B A) (A;B) P(A;B) P(B A)= = ((A)+0, P(A)+0) (A) P(A) A, B P(A;B)=P(A)P(B A)=P(B)P(A B) (P(A)+0, P(B)+0) A, B P(A;B)=P(A)P(B) (P(A)+0, P(B)+0) 4 A p A r P P =«C p r q -r (q=-p, r=0,,, 3,, ) 78

79 (A) P(A)= (S) 0 A, B, C, D, E A B C D ; 5; ; 4; ; 3; ; ; ; ; ; 8; ;!; ;!8!; ;!8#; ;6%; 6_6=36 (, ), (, ), (, 3),, (, 6) (, ), (3, ),, (6, ) (, ), (, 4), (, 6) (4, ), (6, ) (3, 3), (3, 6) (6, 3) (4, 4), (5, 5), (6, 6) 03 0 m, A= - A m (-A) =E E ;6!; ;3!; ;!; ;3@; ;6%; ;3@6@;=;!8!; 0 A, B, C a, b, ca b c ;9!; ; 7; ; 7; ;3!; ;!7!; 79

80 P(A'B)=P(A)+P(B)-P(A;B) A, B P(A'B)=P(A)+P(B) a, b, c, d (a-b)(c-d)>0 ;6!; ;5!; ;4!; ;3!; ;!; A B P(A)=P(B), P(A)P(B)=;9!; P(A'B) ;6!; ;3!; ;!; ;3@; ;6%; P(A)=P(B), P(A)P(B)=;9!; {P(A)} =;9!; P(A)=P(B)=;3!; P(A)æ0 A B 06 A, B, C 6 3 A B A C ; 0; ; 0; ;!; ; 0; ;ª0; P(A'B)=P(A)+P(B)=;3!;+;3!;=;3@; 04,, 3, 4, 5 ;6!; ;5!; ;3!; ;5@; ;3@; 80

81 3 P(A)=-P(AÇ ) 08 X={,, 3} Y={,, 3, 4, 5} ;ª 5; ;;ª 5; ;ª 5; ;!)5@; ;!)5$; 8 ;5!; ;4!5!; ;4!5#; ;3!; ;4!5&; A AÇ P(AÇ )= =;4@5*; P(A)=-P(AÇ ) P(A)=-;4@5*; P(A)=;4!5&; C ºC ; 0; ; 0; ;!; 07 A, B P(A'B)=;!;, P(AÇ )=P(B)+;3!; P(A;B) AÇ A ; 0; ;ª0; ; ; ;6!; ;4!; ;3!; ; ; 8

82 4 (A;B) P(A;B) P(B A)= = (A) P(A) ((A)+0, P(A)+0) 0 S A, B P(B A)=;!;, (A)+P(A)=: 3 : (A;B)+P(A;B) (X) X ;3&; ;(; : 6 : : 3 : : : ;7!; ;7@; ;7#; ;7$; ;7%;,, 3, 4, 5 5,, 3, 4, ;8!; ;4!; ;8#; ;!; ;8%; A, B (A;B) P(B A)= =;ª;=;7#; (A) A, B (P(A)+0, P(AÇ )+0 AÇ A ) A B P(B A)=0 A,B P(B A)= P(B A)+P(B AÇ )= 8

83 5 P(A;B)=P(A)P(B A) (P(A)+0) 3 A, B P(B A)=P(BÇ A), P(A)=;3!; P(A;B) BÇ B ;9!; ;6!; ;3!; ;!; ;3@; A B,, 3, 4, 5 A B A B A, B 0 %, 50 % 3 A 3 B ; 5; ; 5; ;5!; ; 0; ;5!; ;4!; ; 0; ; 0; ;3!; ;5@; X, Y X 5_4 P(X)= =;5$; 5_5 3 3_ P(Y X)= =; 6; 4_4 P(X;Y)=P(X)P(Y X) 5 70 % 0 % MP3 60 % MP3 MP3 ; 6; ; 6; ; 6; ; 6; ;ª6; P(X;Y)=;5$;_; 6;=; 0; 83

84 6 A, B HjK P(A;B)=P(A)P(B) (P(A)+0, P(B)+0) 6 A, B P(A)=;!;, P(A'B)=;3@; P(BÇ ) BÇ B ;3!; ;!; ;5#; ;3@; ;6%;,,,,, ; 7; ;5!4!; ;9@; ;5!4#; ; 7; 4 A, BA, B A 3,, 3 A P(A)= B P(B)=;6$;=;3@; 3_+_+_3 6_6 P(A;B)=P(A)P(B) P(A;B)=; 8;_;3@;=; 7; =; 8; 7 8,, 3, 4, 5 5 a, b a, bab ; 0; ; 0; ;!; ; 0; ;ª0; A, B, C, D,, z, w++z=8 w 3 ;!6; ;%6; ;&6; ; 6; ; 6; 84

85 7 «C p q -r (q=-p, r=0,,, 3,, ) ;!4@3&; ;!4@3*; ;8$#; ;!4#3); ;!4#3!; 채널 채널 채널채널 50 ;4!; ; 6; ;8#; ; 6; ;!; ;!; 3 0 C {;!;}3 {;!;}3 = =; 6; fl ; ; ; ; ; ; ; ; ; ; ;3 ; ; 6; ;3 ; ;8!; ; 6; 85

86 대단원마무리 Level- 0 ++z=77 (,, z), z {+ 'ß } a _b a, ba+b 03 a = C + C + C ++ C a «a« ;7!; ;7@; ;7#; ;7$; ;7%; 86

87 05 a, b, c a, b, cabc 3 ;!7^; ;!7&; ;3@; ;!7(; ;@7); p p p +p ; 5; ; 0; ;3 0; ;4 0; ;5 0; 07 A, B 3 A, B q ;!;, ;3@; A p+q p pq 87

88 대단원마무리 Level- 0 a, b, c, d aæbæcæd A 3B 4C 5 C ;9 9; ;9 9; ;9!9); ;9!9#; ;9!9^; 03 X={,, 3, 4, 5, 6, 7, 8, 9, 0}f:X X <X f( f())=f() {, 3, 5, 6, 7, 0},{ f() <X} X a, b a<b f(a) f(b)

89 04 S (S)= S A, B (A, B) (X)X A'B=S, A;B=u, A+u, B+u (A)<(B) A T TA 0.9 A 0.05 %A TA A ;6!7^; ;6!7&; ;6!7*; ;6!7(; ;6@7); 06 p 0<p< p 3p-3p -p 3p-3p +p -3p+3p -p 89

90 0, X P(X=) X X X X X,,,, «X Xp, p, p,, p«p(x= )=p (i=,, 3,, ) X X P(X= )=p (i=,, 3,, ) 0 p p = P(a X b)= P(X=) i= b =a 3 X X P(X= )=p (i=,, 3,, ) E(X)=m= p V(X)=E((X-m) )= ( -m) p =E(X )-{E(X)} r(x)=" V(X) i= i= 4 ax+b X a, b E(aX+b)=aE(X)+b V(aX+b)=a V(X) r(ax+b)= a r(x) 5 A p, A XX P(X=)=«C p q«(=0,,, 3,,, q=-p) B(, p),, X B(, p) E(X)=p V(X)=pq ( q=-p ) r(x)=' pq ( q=-p ) 90

91 X P(X= )=p (i=,, 3,, ) 0 p p = i= P(a X b)= P(X=) b =a X P(X=)= 4 k (=,,, 0) '+5-, P(5 X 9),k ;3!; ,, X P(X>3)=;pQ; p+q,p q P(X>3)=-P(X 3) P(X 3)=P(X=)+P(X=3) P(X=)=;5@;_;4!;+{;5@;_;4#;+;5#;_;4@;}_;3!; P(X=3)=; 0;+;5!;=; 0; P(X>3)=-; 0;=; 0; p=0, q=7 p+q= P 4 P P X, P(X<) ;!; ;ª6; ;8%; ;!6!; ;4#; 0 X P(X= )=p (i=,, 3, 4, 5) {p },p ;!; ;3!; ;4!; ;5!; ;6!; 9

92 X,, X P(X= )=p (i=,, 3,, ) E(X)= p i= V(X)=E((X-m) ) = ( -m) p i= =E(X )-{E(X)} (, E(X)=m) r(x)=!%v(x) 04 -,, a X P(X= )=p (i=,, 3) { i=,,3} {p i=,,3} _ ;6!; b a ;3!; E(X)=, V(X) X X 3 7 P(X=) a ;4!; b E(X)=5,b,a b ;3!6(; ;9%; ; ; ;!8!; ;3@6#; X a+;4!;+b= a+b=;4#; E(X)=5 05 A, B A B B, X r(x) _a+3_;4!;+7_b=5 a+7b=: 4 : - 6b=: 4 : b=; ; 9

93 3 ax+b ax+b,, X a, b E(aX+b)=aE(X)+b V(aX+b)=a V(X) r(ax+b)= a r(x) , -, 0,, 4 X a (=-, ) P(X=)=[ a (=-, 0, 4), r(-9x+0), a> X X P(X=) 0 ;4!; a a E(4X+0) ax+be(ax+b) ;4!;+a+a=, 3a=;4#; a=;4!; XE(X) E(X)=0_;4!;+_;4!;+_;4@;=;4%; E(4X+0)=4E(X)+0=4_;4%;+0=5 08,,, 4 4 XV(-6X+3) X E(6X+) 93

94 4,, 09 X E(X)=4, E(X )=8 P(X 6)=;aB; a+b,a,b X P(X=)= C p q -, =0,,,,, q=-p B(, p) X B(, p) E(X)=p V(X)=pq, q=-p r(x)=4pq, q=-p X B(0, p), P(X=4)=;3!;P(X=5), E(7X), 0<p< X P(X=4)=;3!;P(X=5) ºC p (-p)fl =;3!; ºC pfi (-p)fi 0_9_8_7 0_9_8_7_6 p (-p)fl =;3!;_ pfi (-p)fi 4_3 5_4_3 -p=;3!;_;5^;_p, -p=;5@;p 0 B{5, ;!;} X Y Y=-X+5, P(Y=3)=; 6; V(Y)=;%; E(X+Y)=E(X)+E(Y) p=;7%; E(X)=0_;7%;=: 7º: E(7X)=7E(X)=

95 5,, X E(X ) , X 4X+V(4X+) V(aX+b)=a V(X) ;!;_;!;=;4!; 3 6, 3, 5, 7, 9, X B{0, ;4!;} V(X)=0_;4!;_;4#;=: 8 : V(4X+)=6V(X)=6_: 8 := , XE(4X-3) 90, X V(aX)=E(X ) a a,,

96 ,,, X a, b X f(), f() X b f()æ0 : f()d= a P(a X b)=:ab f()d (, a a b b) X a, b,x f(),x,, b E(X)=m=: f()d a b V(X)=E((X-m) )=: (-m) f()d a b V(X)=: f()d-[: f()d] =: f()d-m ab ab a r(x)=" V(X) 3 X f() f()= e - (-m) r (- << ),Xm, 4pr r N(m, r ) =m, =m 4 X N(m, r ), Z= -m -m P( X )=P{ Z } r r X-m r N(0, ) 5 X B(, p), X N(p, pq) a-p b-p P(a X b)=p{ Z } Z N(0, ) q=-p ' pq ' pq 96

97 a, b f() X b f()æ0 : f()d= a P(a X b)=:ab f()d a a b b 0 -, X f() f()=a +b a<0 f() ;3@; P{0 X ;!;} ; 6; ;8!; ; 6; ;4!; ; 6; X0 X,X O P{a X a+;!;} a ;8#; ;!; ;8%; ;4#; ;8&; P(a X b)=:ab f()d 0-3, 3 X f() -3, 3 f(-)=f() :) f()d=;4!;, :_@ f()d=;3!; :_-# f()d f() +;!; P{a X a+;!;}=:aa f()d a ;3!; ; ; ;!; ; ; ;3@; [a, a+;!;] O a a+;!; ;!; a +;!; +;!; P{a X a+;!;}=:aa f()d=:a f()d+:!a f()d a 3-a P{a X a+;!;}={;!;- }+[;!;-;!; { } ] P{a X a+;!;}=-a +;#;a-;8!;=-{a-;4#;} +; 6; a=;4#; 97

98 a, b X f(), b E(X)=: f()d a 04 -, X f() E(X )=6, V(X)= :_@ (3 +5)f()d E(X)> b V(X)=: (-m) f()d a b =: f()d-[: f()d] ab a r(x)=" V(X) 0, X f() X ;4!; :) (a+5)f()d=0, a b E(X)=: f()d a :) f()d= E(X)=;4!; :) f()d=;4!; :) (a+5)f()d =a:) f()d+5:) f()d =a_;4!;+5=0 a= X X f() E(-3X+5) -0 0 k k =f() _0 O , X f()=;!;, V(9X) 98

99 3 =m =m X N(m, r ) Z= X-m r N(0, ) X N(m, r ) ;5!;X P(X 80)=P(Xæ0) m+r X N(m, r ), a=p(xæm), b=p(-m X m), c=p(0 X m) m>0 a>b>c a>c>b b>a>c b>c>a c>b>a X N(m, r ) P(r X-m r) P(0 Z )=0.343, P(0 Z )= =m m+r V{;5!;X}=; 5;V(X)= V(X)=r =5 =m 80+0 m= =00 m+r =00+5=5 08 X, Y N(m, r ), N(m, r ) f(), g(), m >0, m >0 f{ m }<f(m ) r =r f(m )=g(m ) r <r, m =m, f(m )=g(m ) P(Xæm )<P(Yæm ) 99

100 4 X N(m, r ) X-m, Z= N(0, ) r A N(m, ), B N(m, 4) A B, A k 09 mg, 0 g 98% 90 g, m z P(0 Z z) B k ;mk;; : 9 : ;4%; ;@8#; ;3$6&; ;3$; A X X N(m, ), B Y Y N(m, ), X-m k-m P(Xæk)=P{ æ }=P(Zæk-m) Y-m k-m P(Y k)=p{ } k-m k-m P(Y k)=p{z }=P{Zæ- } k-m=- k-m, k-m=-k+m Z P(0 Z )= _ _ _0.98 5_0.48 5_0.48, 3k=4m ;mk;;=;3$; 00

101 5 X B(, p) X N(p, pq) q=-p 3 z P(0 Z z) A % 0 B 8 C 5 D C 4 z P(0 Z z) C ; 0 0;=;4!; C XX B{9, ;4!;}, 9 X z P(0 Z z) N{9_;4!;, 9_;4!;_;4#;}, N(48, 6 ) 4-48 P(Xæ4)=P{Zæ } 6 =P(Zæ-) =0.5+P(0 Z ) = =

102 X X mr r X, X, X,, X X, S, S X +X +X ++X X = S = {(X -X ) +(X -X ) ++(X -X ) } - S=!#S m, r X E(X )=mv(x )= r(x )= X r N(m, r ) X N{m, } X N{m, r } r r ' N(m, r ) Æ m r r 95 % [Ǣ.96, Æ+.96 ] ' ' r r 99 % [Ǣ.58, Æ+.58 ] ' ' r s 0

103 m r X E(X )=mv(x )= r r(x )= r ' 0 0 X S X =0 E(X +3)=3 V(X )=S X P(X=) ;!; a ;!;-a X X 8 P(X =0) ;5@; ;5!0(; ;ª5; ;5!0&; ; 5; E(X )=m E(X )=E(X)=8 E(X)=0_;!;+0a+30{;!;-a} E(X)=0-0a=8 a=;5!; X =0 0 30, 0 0, 30 0 P(X =0)=P(X=0)_P(X=30) =+P(X=0)_P(X=0) =+P(X=30)_P(X=0) 0 N(m, 5 ) 6 X, X,, X Y Y=X +X ++X E(Y)=80 V{;mY;} m =;!;_; 0;+;5!;_;5!;+; 0;_;!; =; 0;+; 5;+; 0;=;5!0&; 03

104 N(m, r ) X N{m, r } 03 N(0, r ) X P{ X -0 4r 0.5}æ z P(0 Z z) X Z c P( Z >c)= P(Z>a)=0.05a c>a P (X c+75)=0.97 P(X >b)=0.0b c<b-75 P( Z c)=-0.06=0.94 P(0 Z c)=;!; P( Z c)=0.47 P(Z>a)=0.05 P(0 Z a)=0.45 P(0 Z a)<p(0 Z c) a<c m=75 r=5 =5 E(X )=m=75 V(X )= r =;@5%;= X N(75, ) P(X c+75)=p(z c) =0.5+P(0 Z c)=0.97 P(X >b)=p(z>b-75)=0.0 P(0 Z b-75)=0.49 P(0 Z c)<p(0 Z b-75) c<b X X P(X=) 0 44 Cº 3 C 3 C 3 5 X P(X æ73.) z C P(0 Z z) 04

105 3 N(m, r ) X N{m, r } N/m 3.5 N/m N/m N/m z P(0 Z z) X m 4 P(m X a)= a- a cm z P(0 Z z) X N(m, 4 ) m-m X-m a-m P(m X a)=p{ } a-m P(m X a)=p{0 Z }= a-m P(0 Z )=0.343 = 4 a=m X X N{m, } N(m, ) 6 P(X æa-)=p(x æm+) X -m (m+)-m P(X a-)=p{ æ } P(X a-)=p(zæ) P(X a-)=0.5-p(0 Z ) P(X a-)= P(X a-)= X X 50g 5g X 0 P{X 45+ }æ0.95 ' z P(0 Z z)

106 4 N(m, r ) N(m, r ) Æ m 95 % r r [Ǣ.96, Æ+.96 ] ' ' 99 % r r [Ǣ.58, Æ+.58 ] ' ' 07 Æ g, g 99 % 7.355, _Æ,Z P(0 Z.58)= ) % mm Z P(0 Z.96)= % 00 r s, s=0, =00, Æ=45 m 95 % 0 0 [45-.96_, _ ] , , 43, 44, 45, 46, 47, r Æ m 95 % Ǣ r m <,Z P(0 Z.96)=0.475 )

107 5 a, b b-a a, b, b-a 95 % a, b b-a r _.96_ ' 99 % a, b b-a _.58_ r ' m a %, 9 a z P(0 Z z) m 95 % a m b, b-a P(0 Z.96)= r b-a=_.96_ b-a ' 600 r s s=6, =600 6 b-a=_.96_ = r 5 95 % a, b, 99 % c, d b-a d-c,z P(0 Z )=0.475, P(0 Z 3)= N{m, ;4!;} m 99 % a, b b-a=0.9 Z P( Z.58)=

108 대단원마무리 Level- 0,, 3, 4, 5 X a (=,, 3) P(X=)= g b (=4, 5) A={X Xæ3}, B={X X 4} P(B A)=;4#;, E(8X+4) X X 0 3 P(X=) a ;8!; ;4!; b P(X )=P(Xæ), V(X)=;pQ;, p, qp+q , XE(X)=0, P(X=3) P(X=7) , X f() -, f(-)=f() E(X )=;5!;, f{;!;} ;8#; ; 6; ;!; ;ª6; ;8%; 08

109 05 a N(, ), + = a-= z P(0 Z z) X, V(0X), Z, P(0 Z )= g, r g 700 g 6900 g, r %, % 4, k k, Z,P( Z.96)=0.475 )

110 대단원마무리 Level- 0 X B(3, p)p(x=)=p(x=) V(X) 0<p< ;6!; ;3!; ;!; ;3@; ;6%; 0 XY X 3 Y 4 9 P(X=) p p ;!; P(Y=) p p ;!; V(X)=;9%; E(Y) , XV(X)=9 {,, }

111 04 N(0, ) Z P(0 Z a)=p a a X N(5, 4) P(3 X 6) p -p ;!; p +p ;!; p -p ;3!; p -p ;!; p +p ;5!; 05 0, c X f() A=[ f() ;!;] P(X<A)=;6!; P(a X b) 0<a<b<c ;6!; ;4!; ;3!; ; ; ;!; O =f() a b c 06 X X 60.5, z P(0 Z z)

112 memo Educatioal Broadcastig Sstem w w w. e b s i. c o. k r

113 C otets EBSi Q&A

114 3 + +(-4) + +(-4) 3 0 A= AX=XA= 0 X :_! d+:@- d + + '8 3 " 4 '4-0 -: : -5 ;!; ' ' ' -;%; 0

115 5 0-8 {a } (a 3k- +a 3k- +a 3k ) k= {a }{b } a =b = a + =a b b + =a b log a +log b X X P(X=) ;!; fi a E(6X-0) (-) 0 {+;[A;} 0 a ' ' ' 3

116 9 f() f() f() =-9 - = % A(Aæ70) B%A B A=70-k+logå {B+;; 3º;;} (, a>0, a+, k ) 80, % AB P(A'B)=;!;P(A B)=;8#;P(B A)=;!; P(A) ; ; ; ; ; ; = + P(tt +) P P tob A B t OA t>0 O = `+ ; ; ; ; B P(t,`t `+) O A ;4!; ;!; ;#; 4

117 3 A 3 B 3 A B A ;!; ;!8%; ;7$; ;!8&; ;ª4; A= p, q - (, E) A -A A+pE A -qa-q E,,,, 4 A B = B =90 B A C A C A, A B =A A B =90 B A C A C A, C, C A C A A B =A A B =90 B A C A C A, C, C A «C«A«, A«B «=A«A «B«=90 B«A«C«A C A«, C«, C«, C «C «= B B B B A A A C A C C C "3 ' ' A % 46 B C 5 80 % 00 C 60 z.0 P(0 Z z)

118 7 {a«} S«= a«= S«S«+, S«+0, S«+ ;!; k= a, {a«} 8 O ='ß P(t't ) OP =PQ QPQ =QR R OR ='ß t OP PR a«=s«-s - S«S«-S - = S«+ (S«-S - )(S«+)=S«S«= + S«S - = = = S a S«S«= a«= (æ) R =/ß P O Q 'ß3 'ß 'ß3 ;3*; 3 a«= (æ) (=),, p, f(), g() p, f~(0)g~(0)

119 9 f()=: (3t- t +)dt f()= -a +a+ =;3@; - f( )= a ;3@; ;3$; 3 4 ;3*; : 3º: =,={;4!;} -m A, =,={;4!;} -m B, CAB =AC, m O = A B C O ={;4!;} _m 'ß- 3log 3log '5-3 '5-3 3log '5-3log 3log '5- '5-7

120 3 log log ;!; =8 log ;!; +5 5 {a«} a +a +a ++a º=53 a +a +a ++a ª=7, a +a +aª+a +a =;pq;, p+q (, p,q 4 :)4-6 d 6 f()= -k+6 (af(a)) = ak a+k 8

121 7 [0 ] X - 9 A= 0 - f() E(X)=;3@;V(X)=; 5; a«b«:) ( )f()d A = =3 c«d«a«+d«00 c«-b«8 (æ3) ( -) - +=0a b a -b =a a =;pq; p +q pq =3 30 a ;a!; a'a f()=(a ) og -;8!;, f(a'a) 9

122 ;4!; _ -;4!; _log 4 ;!; ' ;4!; ;!; ;4#; ;4%; ' AB A = AB= (A+B) - = - 3 A h 0 f()= f(+h)-f() h

123 5 0 3 =t 4 9 t <0) a, b Pº t P P ={;A;} ;bt; Pº (Pº>0).3 30, ;!; (,, log.3=0.39, log =0.300 ) X X 0 a P(X=) b ;!; b E(4X+)=7 ab ab ;3!; ;!; {a } -a = ;7%; ;7$; ;7#; ;7@; ;7!;

124 9 f()=;3!; g() (f Á g)() g() = = g() 0 f(+) = f()g() 4 3 =f() 4 3 =»() g()+g(-) O O f()+g() g() f() f()g() 0 ;#;-(+)= a a ;6!; ;3!; ;!; ;3@; ;6%; f()= + f() f(3) ()

125 3 PP 3 P 5 ; 8; ; 4; ; 8; 5 X, Y 3 X+Y=E, XY=O, px+qy= 4 (, E,O, p, q p>q) ;7!; ; 8; X =X YX=O p=,,, 4 ABC ACB=90, AC =, BC = BC A A AB AC B, B AB C C BC A A AB AC B B AB C A«, B«, C«A«B«C«S«S«{A C +;3!;} A C C B 6 5 log log 3 = ;4$5^; ;4$0!; ;3#5^; B A A A B C ;3#0!; ;@5^; ;9!; ;3 6; ;6!; ;3 6; ;9@; 3

126 7 {a«} a =3 a«=a -;!;a +;3!;a -;4!;a ++(-)«± ;!;a«8 (=,, 3, ) a«æ a«=a -;!;a +;3!;a -;4!;a ++(-)«a - -, a«=a +(-)«± ;!;a«+(-)«± a«= a«(æ) a =a =3 a «= (æ) a «= = (æ) a«= p, f() f(p) ;5^; ;5&; ;5*; [단계] [단계] [3단계] 시작 머리 5층 4층 3층 층 층 : 성냥개비 ;5(; 9 80 g 0 g 6 00 g 600 z P(0 Z z)

127 0 f()= +a +b+c f'()=0 { -;[#;} 4 ab (a<b)0 abc f'(a)>b b=3 a -3 f(a)f(b)>0 f()=a f()=:)/ (at +bt+a)dt f()= f() f(a) a+0 ab 3, {a«} a +a +a +a =40, a +a +a +a º=58 8 = a

128 ={;!;} -4+ = -3+=6 -+k 4 +5 k 6 5 f()= +5+4 f() k 9 6 f'{+ } <f()< k= (5 +3)f() 6

129 A B m 0 P 3 Q 5 z P(0 Z z) Q P A B 34 a b b-a B 4 B B 3 B 4 P A B Q ;pq;p+q pq 30 A (0, a ) = a 3 {a«} A«(0, a«), A«= B«B«B + b«, 85 = =;pq; p+q b«(, A =B,p,q ) = A«B«A A A O B B B 7

130 3 6 ;4#; +log f() -;3@; -;3!; 0 ;3!; 3 f()-f(3) -3 ;3@; h 0 f(3+3h)-f(3) h = 3 " ;4#; ;3$; ;#;

131 5 {a } a =a =9a 7 f() 5 a 3k- k= : f()d={ f()} :) f()d=;8(; :_@ f()d a A= A =A - b a b a+b Mº g t M g T M=Mº{;!;} ;tt: 63 ;5@; a a log =

132 3 9 X log ;3!; (-5)>log ;3!; (+7) X 3 P(X=) a b c P(X=)=P(X=)=;!;P(X=3) X abc ;4#; ;4(; ;%; : 4 : ='ƒ+3 =3 =t (t>3) ABB =3 BH H t 3+0 AH 0 f()= +a +b (ab) (f()) (-f(-)) AB AB =4b O A = B H +3 =t =3-4 -;(; -5 -;; ;; -6 ;4!; ;3!; ;!; ;3@; ;4#; 0

133 3 =- =(-) 5 8 ;3!; ;3@; ;3$; ;3%; {a«} S«S«=;#; a«- (æ) {a«} a«s«=;#; a«- (æ) = S =;#; a - S =a a =;#; a - a = S + =;#;a a + += (a«+) 6 f()= a g()= ++a t =f()=g(-t) a a«= f(), g() f(5)+g(3)

134 7 3 5 = =-+ P«Q«=-+ H«P«Q«=;:; a«oh«b«'3 ;3!; ;!; 3 ' '3 O P«=_+ H«b«a«Q«9 f()g() =f() _ O O _ { f()+g()}= +0 { f()+f(-)}= -0 =»() f()g()(0, ) 8 AB AB+B=E3AB+BA=A-B (E) B - =;!;(A+E) AB=BA A - =;!;(E-3B)

135 0 Aº(6, 0) C '3 l 3 lc C C, C, C l a lc C C, C, C l a a«a«= l N(ab) X f() N(cd) Y g() g(-)=g() f()=g(-3k) P(X 7k)=P(Y 3)=P(Z ) abcd a+b+c+dk Z : 4 : : 4ª: : 4 : : 4 : : 4 : O C C C Aº(6,`0) (9-5'3 )p 8-9'3 p (9-4'3 )p 8-7'3 p (9-3'3 )p f() f() - =;!; f() f() =

136 3 3 {a«} a =-5 a«=a«+(+) a 5 98 a 64 X z P(0 Z z) P(96 X 00)=0.68 a P t v(t)=t - P p60p 6 =log (+)= ( ) k >00 k= =log (+) 4 3 O «4

137 log f() g() q p+q p p q f() f()=f() g() log ;; 3º;; 8 a 4 a+b = 3b a- b+3 =0=0 a +b ab 30 {+ } - fi - a a a a - a k- =4 5 k= 5

138 4 3 0 'ƒ3+- + log 0+log log log 3 log log 5 log 5 ;!; ;4#; ;#; - A - = B= - (AB - ) - A - A AB P(A)=;!;P(B)=;3!; P(AÇ 'B)AÇ A ;6!; ;3!; ;!; ;3@; ;6%; 6

139 5 {a } a () a + =g a () a º+a =30 a [0a] X f()= -a +b E(X)=;!; ab a+b ;4!; ;!; ;4#; ;4%; 6 f() :)/ f(t)dt=3 + :) f(+)d {a } a«+ a«+3 a«- a«+ =;!; ;3!; ;!; 3 7

140 9 f()= 4 + +a + a ;7@; ;3!5@; ;3!5^; ;3!5*; ;7$; 0 0 A ab - a 36 A = a+b b I C K I=a+Klog C a AB pq A B AB pq log q 34 log p p>q> ;!; ;3@; ;4#; ;5$; ;6%; 8

141 3 N(mr ) 5 f()= +P X Q g()= m m 98 % z P(0 Z z) [X -dx +d] a % [X -;!;dx +;!;d] a RS PQSR PQRS P PQ f()g() P Q f()= +»()= P Q R S O 4 {a«} a {a«} k= k= a k+ ;!; = a ;!; S«= a a =S -S (kæ) k= k= a k+ a S -S a = + k= k+ - S S«S = + - k= k+ + k= k+ - S - S S«= - + k= k+ k= + - S«= S + k= + S«ab a+b a + b a - S«S + k= k+ k= =;!; k= + f(k)g(k) f(0)_g(0) ; ; ; ; ; 3; ; 4; ; 5; 9

142 6 4 A A =A A E A A-E A = + +0, 8 A(, 0)B (0, ) B C AB OC B B C AB OC B OC«B«S«S«O = B (0, ) C O B C B C B A(, 0) 7 f()= 0 - g()=0 - f() f()= f()=g() 9 P«(0) P«(+0)Q«()Q«(+) P«P«Q«Q«D«OP «Q «D D D D «a«a º O ;(; ;; 4ª;; 5 ;; 4 ;; ;; ;; 30

143 0 f() g()=( (>) g()={ f()(- ) g()=9 - (<-) A«={ f(0) f() g() } {a«} S«p(+) S«= {b«} a«b«=s «(=3) b p0 A ={0} 0<A A 'A =A k f()= -3 +k g(k) g(k) 5 k= 3 f(0)+f() f() f() :) f'()d=: d f(0) f(0)+f()

144 4 4 {a«} a +-<a + <a ++ a «=0 6 f()=log =g() (g Á f )()=+'ƒ9- [g{;4%;}] a «7 P º «º «P ; 0; 5 f()= - =a =a+ =a- a m 0m ;ª0; ; 0; ; 0; P A= ; 0; ; 0; «º =A««º - -3 º - =;ab; - -3 º ab a+b 3

145 8 f()= -a g()=;!;( -a + -b ) : f()d=:0 g()d ab 0 a+b 0<a<b< A 6B 3 X ;3!;E(X) B abc a +b +c B 9 A E [ ] [ ] 3456 A B C D E A B A E 4 q B p p+q pq 33

146 5 log ;!; 4+3 log :_a! (-)d=6 a A= B= 3 3 B+X=(X+A) X 4 = +a 3 =; 0;a

147 { - } 0 7 -{ - } 0 G G A A AB P(A)=;!; P(B)=;3!; P(A;B)=;4!; P(AÇ BÇ ) AÇ A ;4!; ;8#; ;!; ;8%; ;4#; 8 f()=;3@;a +b +;!;(4-a)+3 (ab) 4p 6p 8p 0p p 35

148 X X P(X =) ;9!; ;9@; p q ;9!; E(pX +q) pq {a«} 0 a =0, k= m a =50 a =0 m k= 0 k= ;9*; : 9º: ;3$; : 9 : : 9 : =f() =g() 0 = A(-)B(4) C(tt ) -<t< _ O _ =f() O _ =»() 4 = B A C _ O f()+ g()= =f()+g()=- =f()g()= 3 : 8 : : 4 : : 8 : ;&; 36

149 3 f() P(-f(-))Q(f()) PQ f()=- p (p>0) :_aa f()d=f(0) a :_! f'() d=p :) f() d<:) f'() d 4 {a«} a =0, a«-(+)a«= (=,, 3, ) + a«= (+)a«a«-(+)a«= (+) + a«a«- = (=,, 3, ) + (+)(+) æ, a«- =a + k= k(k+)(k+) - =;!; [ - ] k= k(k+) (k+)(k+) =;4!;- a«= (=, 3, ) = ;3$; { - } = (+)a«k= k- =;3$;_;; 6 ;;=;; 9 ;; f() g(k) _ f(3) g(3)

150 5 5 A A B=A+A E AB=BA B A =-A B+E 7 f()=;!;(3-3 - ) g() g() 0 log ('-) log (+' ) log ('-) log (+' ) 6 A B C D T S A B C D A B C D T S A B C D A B C D T S T«S«S«= A D A D A D A D A D A D B C B C B C B C B C B C T T T 8 A 00 g 0 g A 0 g p z P(0 Z z) 4 k g p p -p =0.099 k ('-) 4('-) ('3-) '+ '3+ 38

151 9 {a«} 0 f()= -3 +k k 3 4 m b m 0 m= bμ-a a a a a 0 a a a a aª 4 ;ª0; ;!); ;5(; a º f'() = f() 0 k= æ0f()æ0k 4 ;@); : 6 : t A A=k "ça t ak f() f() -+3 f() = =6 'ƒ+3- f(3)

152 5 3 O = + 5 f() f()=3f'()=- P«( 0) 4f()- f() OP«d«0d«- = `+ P«d«O a a a a a a X B{00;!;} Z N 0 P X k =P Zæ3 k 0 k<50 ;pq; pq 0p+q 40

153 = =;;3;; 7 9 {a«} S«= a i= ==3+ S km = k a º A«B«C«D«A«B«C«D«Sμ m a º 8 q a«a«=n log 3 N 0p+q p = pq = =;3; D«C«=3+ A«B«= O 8 f()= a =-+ (k=) P«=;!;{ f(a )+f(a )++f(a«)} 3 P«3k 30 [ ] a b PQ c d PQ A 980 [ ] A B a c b d p r q s A a(q-p)+b(s-r) b-a 4

154 A= B= AB 4 0 ( ' 8k+log ;!; 5) k= (4+) (+)(-) 5 3 {a«} {b«} b«=a«-a«(=3) {b«} h 0 f()= +a f(+h)-f() h =3a X X P(X=) a ;!;a ;4!;a ;8!;a ; 6;a E{;5!;X+} ;3$#; ;3$%; ;3$&; ;3$(; ;3%!; 4

155 7 85 æ -5 æ t T(t)(æ) T(t)=-5+cp t kcp -5 æ85 æ 0 5 æ 85 æ 40 0 AB P(B)=;3!;P(A BÇ )=;!; P(A'B) BÇ B ;6!; ;3!; ;!; ;3@; ;6%; æ 3 æ 5 æ 7 æ 9 æ 8 {+ } f()g() f()=6+;3!;:) g(t)dt N(50, 4 ) 50.5 f() f(6)-f(00) z P(0 Z z) g()=(+)f(-) :_! f()d

156 6 =;[!;= A() =a (0<a<) =;[!;= BC B = D S ABCADB S S a -0 S O S C O B =a S A = D =: : 4 A (6)B (6) P Q A P +PQ +QB PQ P Q l O OA OB P Q A B A P +PQ +QB PQP Q l OA OB P Q A B A«P +PQ +QB«P Q P«Q«l«OA«OB«P«Q«A + B + l«= B (,`6) ;#; ;3%; : 6 : Q Q B B A A A (6,`) O P P ' 4' 6' 8' 0' 3 ABC P ;3!; PA 3 C B B A C ;5!; ;3!; ;5@; ;!; ;5#; 44

157 5 A E O A«=E A A«+O A A A«+O 7 S«=+;!;+;3!;++;!; S =-;!;-;!;S«` k= k(k-) ==;4#;, =;4#; =m, m S =- - Sμ k= k(k-) m m m+ S k= k(k-) m = S + Sμ k= k(k-) =- - (Sμ - )+ Sμ m m =- - Sμ m+ m+ =m+ f(m)g(m) - f(0) g(0) 6 A={ >0}, B={ }, C={z 0 z<} fgf A B g A C A 0 f()+g() = Aa b f(a)=4, f(b)=3, f(ab)=8, f{;ba;}= a g(a)<b a b M, m0m+40m

158 8 6 -<< =f() a (-<a<) g(a) g(a)={ f()}_{ f()} a+0 a-0 g(a) 0 {a«} S«{S«} æ S =(S + -S - ) S - =(-)a«=f() O _ - -<t< t g(a) a t =6 A(6) l A A m lm 9 f() f(-)=-f() :#6 f()d=3:)6 f()d=-5 :_0# f()d

159 [0] X f() :) (+3)f()d=: 3 ::) (3 -)f()d=;6%; X ;pq; p+q pq 3 ;4!; 8 =log ;!; { } log ;!; +log M m M-m 6 f()= +3 +3a =a =b f(a)-f(b)=b-a 00a a 4 :) (6+)d-:$ (6+)d 47

160 7 6 AB =AC =0, C A=90 ABC P P BC, 0 a P CA, AB abc b c a b A c a 0 l P l p B 9 A(305)B (530) B C C A B B«C«C«A B«B«a«a«C B C C O B B A 8 - A= - 0 A+A +A +A +A - +(A - ) +(A - ) +(A - ) =aa+be ab a +b A - AE 30 > log f()g() ;!; f()= g() a«a«0 = 48

161 대단원마무리 Level 대단원마무리 Level 대단원마무리 Level 대단원마무리 Level

162 대단원마무리 Level 대단원마무리 Level 대단원마무리 Level- 대단원마무리 Level 대단원마무리 Level 대단원마무리 Level

163 =, + =4 +0 a=0-0 b=-5 a-b=5 +-6 = =0 4 (-)(+3) = =-5-0 -(-) 0 f()= ( +a+)=a f()= (- ++b)=b f() b=a+ a +b =a +(a+) =(a+) + a=-, b=,a +b 5 = f() -<a<a k = -+ =4 05 (g Áf )()=g( f())=3 + (fág )()=f( g())=(3+) - = = = (gáf )()-(f Ág )() - (3 +)-(3+) - -6(+) = - (-)(+) O = f() (-) (+) (-) a f() 4 03 f()=, f()=- f() =f(-) =f() +0-0 f(-)=0, f(-)=0 f(-)= +0 f(-)= -0 t --0 t -+0 f(-)=0 f(t)=0 f(t)=0 = f() O _ =f(_) 06 ;[!;=t =;t!; (3-)[{;[!;} 0 +{;[@;} 9 ++{;[(;} 0 + ] 3-t = {t 0 +(t) 9 ++(9t) +0t} t +0 t = (3-t)(t 9 + t ++9 t+0) = ;[#; = Æ 4+;[!;-;[!:+Æ -;[@;+;[ #: = =;3@; t !%4 +-+!% -+3 3

164 08 =-t - = = Æ +-;t!; = t -+;t!; + = - =- 09 =-t (fi +a)fi+!% +a - = fi(t -at)-fit!%t -at = (fit -at)-fi!%t (t -at) = (!#t -!%t -at )( a>0) = = = t t t t t t t =;A; ;A;= a=4 a +!% !%t -3t+ -(t-)!%t -3t+ +t- -t+ at!#t +!%t -at a +Æ -;ta; 4 a=3 f()+g() =h() f()-g() {h()-} f()={h()+} g() g() f() = g() h()- = =;4@;=;!; f() h()+ g() - f()-g() f() = 3=;5#; f()+3g() g() +3 f() p=5, q=3 p+q=8 8!% -++a 3 =b (!% -++a)=0!%(-) -%(-)++a (-)=0 a= a - - b=;4%; h()- h()+!% a+b=+;4%;=: 4 : = =;4%; - -(+)(3-) (+)(!% -+-) 0 f()-g()=h() g()=f()-h() g()= { f()-h()}=5-=3 {3f()+g()}=5+6= a+log f() a+log 3 (-)(a+log ) +- (-)(a+log ) +- (-)f() =a +- a=6 (-)f() +- (-)(a+log 3) +- (-)(a+log 3) =a, =a +- 4 f(-) = + (-)(+) f(-)+g(-) - f(-) (-)(+) g(-) (-)(+) f(t) = t 0 + t(t+) =-;#;=-;!; g(-) (-)(+) -=t -=s s g(s) (-s)(3-s) 4

165 5 f()=(-)(+)(a+b), a>0 f(0)=-b=3 b=-3 f()=(-)(+)(a-3) f()f(-) f() f(-) = _ =-8 (-) - - f()f(-) [- ] (-) f() -f(-) = _ - - f() f(t) = _ - t - t+ = (+)(a-3)_ (t-)(at-3) =(a-3)_(-)(-a-3) =4(a -9)=8 a =6 a=4 ( a>0) f()=(-)(+)(4-3) f()=5 6 f(g())= f(t)= -0 t +0 g( f())=g()=3 +0 f(g())+ g( f())=+3= t g( f())= f(g())= g( f()) =g() 4 f(g(+4))=f(g()) =f() = g( f(+4))=g( f(-)) f(g(+4))= f(g())= f(t)=-, f(g(+4))= f(g())= f(t)=- f(g(+4))=- g( f(+4))= g( f(-))= g(t)=0, g( f(+4))= g( f(-))= g(t)= g( f(+4)) f(g(+4))+ g( f(+4)) = `_ P(, ) a =a(-) P _ O _ =a(_)+ =a(-)+(-, 0) a=;3!;, (0, ) t -0 t -0 t -0 t -0 7 f( f())= f(t)= -0 t +0 f( f())=f()=0 f( f())= f(t)= 3+0 f( f())+f( f())+ f( f())=+0+=3-0 8 f(-)=f(+) =f() = g(+)=g(-), g(+4)=g() =g() 4 f()g()=, f()g()=0 +0 f()g()+0 f(g())= f(t)= f(g())= f(t)= t 3-0 f(g())= t -0 g( f())= g(t)=, t g( f())= g(t)= t -0 t -0 a=0 a=0, f(0)=3 0<a<;3!;, f(a)=4 a=;3!;, f {;3!;}=3 a ;3!;-0 f(a)=4 0 l -t =-;t!;(-t) =-;t!;+t + A(0, t +) OA =t +, OP =!%t +t (OA -OP )= t t (t +-!%t +t ) t + = t =;!; t ++!%t +t 5

166 =;!; +4 P{t, ;!;t +4} l m l -{;!;t +4}=m(-t) =m-mt+;!;t +4 ;!; +4=m-mt+;!;t +4 ;!; -m+mt-;!;t =0 D D =m -4_;!;_{mt-;!;t }=0 (m-t) =0 m=t l =t-;!;t +4 l=a + a + a -t+;!;t + D =t -4a{;!;t + -4}=0 a (-a)t =;a$;-6a =t-;!;t +4-4=0 D 4(-4a ) 4(+a) t = = { a+;!;} a(-a) a t =6, t=4 m=t>0 a ;!; a ;!; a a ;!; a (t +t+8)=6+8+8=3 3 f()=;!; +4 P{t, ;!;t +4} l f '(t)=t l -{;!;t +4}=t(-t) =t-;!;t +4 a 0 0 f() = f()=a =f(), f()=a+3 a =a+3 a -a-3=0 (a-3)(a+)=0 a=3 a=- a 0 - si ;[!; - si ;[!; - + si ;[!;+!% +-!% +- +!% +- 0 {- + }= (- +!% ++)=4,!% { + }= 0 ( +!% ++)=4!% +- 0 { si ;[!;+ }=4!% +- f() =0 f(0)= 0 { si ;[!;+ }!% +- a= f() =0 0 b=!#a f()=f(0) a=b a, b 0 0!% + +a -b «!% + +a -b «= = =;4!; =;4!; 0 0!% + +a -a «(+) «(!% + +a +a) 6

167 =3, ; a;=;4!; =3, a=b= a+b+=++3=7 04 g( f())= g(+a)=g(a)=a -3a g( f())= g(3-)=g(3)=5 +0 g( f(0))=5 a -3a-4=5 a -3a-9=0 (a-3)(a+3)=0 a=3 a=-;#; 3+{-;#;}=;#; 05 g() =, =3 = g()= g()=g() g()=(4+a+b) 3, g()=(4+a+b) 4 (4+a+b) 3=(4+a+b) 4 4+a+b=0 = g()= g()=g(3) g()=(9+3a+b) 3, g(3)=(9+3a+b) 3 (9+3a+b) 3=(9+3a+b) 4 9+3a+b=0 a=-5, b=6 a+b= 06 f(-)g(-)= f()g()=(-)_(-)= f()g()=_= f()g()=f(-)g(-) f(g(0))=f(-)= f(g())= f(t)= -0 f(g())= t -+0 t -+0 f(t)= 0 f(g())=f(g(0)) g()=(4+a+b) 4, g()=(9+3a+b) 4, g( f() )=g()=0 g( f() )= g(t)= g( f() )= g(t)=0 g( f() )=g( f() ) 07 <, =0 «+a f()= =;A; «+ >, =0 a +4 «+a «f()= = 4= «+ + «=, +a f()= 3 f() = ;A;== a=4 08 <, =0 «± +si a f()= =si a «+ >, «+a 3 «=0 t -0 t -0 4 si a + «f()= = +4 «=, +si a f()= =-, --si a f(-)= f() =, =- +si a --si a = =si a, -si a= =- si a= 7

168 a= p 0<a p ;5!;< ;4!;, 4 ;[!;<5 f()=4 09 = _ = _3 ;4!;< ;3!;, 3 ;[!;<4 f()=3 ;3!;< ;!;, O 3 4 ;[!;<3 f()= >, -3 < - f()=- <, - < -3 f()=-3 =, f()=0 f() = f()(-, k),k a > b, b < a =0 a «± +b «± =a a «+b «a < b, a < b O 3 a «± +b «± a «+b «b «a «a «b «=0 =f() 3 a «± +b «± =b a «+b «0 ;5!;<<5 ;5!;<;[!;<5 [;[!;] 0,,, 3, 4 ;!;<, ;[!;< f()= fi <<5, ;5!;<;[!;< f()=0 f() =;4!;, ;3!;, ;!;, 4 f() = f()= f()=f() =, = 4+a f()=, f()=+a, f()=b -0 4+a a=, b=3 a +b =0 =+a=b 0 k=-, = f()- f()+k k f(g())= f(t)= +0 f(g())= f(t)=0-0 f(g(0))=f(0)=0 f(g()) =0 { f()-}{g()+4}= t -0 t +0 { f()-}{ g()+4}=0-0 O = f()_ 3 8

169 { f()-}{ g()+4}=0 { f()-}{ g()+4} = 대단원마무리 Level f()=log +- f() (0, ) f()=log +-=-<0, f()=log +-=log >0 f()=0(, ) 4 g() g(-)g()<0 g()=0(-, ) f()=- g()=f()+ g()=- + g()=0(-, ) g()= f() -3 f(-) g(-)= f(-) -3 f() =-;3!;>0 g()= f() -3 f(-) =;!;-3<0 g(-)g()<0 g()=0(-, ) g()=si f()+cos f();4; p`<<;3; p` g(-)=si f(-)+cos f(-)=si +cos >0 g()=si f()+cos f()=-si +cos <0 g(-)g()<0 g()=0(-, ) (-, ) -5 0 a =- - a-5 =- a- a-5=-a+ a= -4 (-)(+) = =;3*; -- (-)(+) ;[!; {5++ } - 5+ (-)+5+ = 0 [ ] - 5+ (-) -(+) = 0 (-){(-)-5+ } 5+ (-3) = 0 (-){(-)-5+ } = =-;#; 03 f()=(-a)(-3a)(p+q),p+0 a 0 ap+q=-;a!; 3a 3ap+q=;a!;, p=, q=-;a@; a f()= a (-3)5+ (-){(-)-5+ } f() -a f() -3a f() -a =-a(ap+q)= =a(3ap+q)= a =- (-a)(-3a)(-a) f() 04 f()=(-)(+p) - 9

170 {!%f()-!%f(-)} = {!%(-)(+p)-!%(+)(-p)} si ;5; p` f() +4+cos ;5; p` Æ +4+si ;5; p`-+!%f()-+ {Æ +4+si ;5; p`-+}=3, (p-) =!%(-)(+p)+!%(+)(-p) =p- p-=3 p=4 f()=(-)(+4) f(0)=-4 {Æ +4+cos ;5; p`-+}=3 {!%f()-+}=3 Æ +4+cos ;5; p`-+ AB =AM AM A OP OP -t = t, (-t)-t=0 AB =_ BP =(t-), AB = t +0 AB BP / `+ `= _/ _/ -t!%(-t) +t 8(t-) = 4 t -t+ =4 t +0 (t-) O M B A(, ) P (t, _t) += 8(t-) t -t+ 4 + =r P(a, b) a+b=r / 06 f() =0, = 0 g() g() =4, =0 (-) (-) g()=g(0)=0, g()=g()=0 g() g()=(-)( +a+b) a, b 0 0 g() (-)( +a+b) = (-) 0 (-) = ( +a+b) 0 =b=4 g() (-)( +a+b) = (-) (-) = ( +a+b) =+a+b=0 a=5, b=4 g()=(-)( +5+4) g()=(-)(+)(+4) g(3)=3 4 7= A + =+= A (, ) PB =PA =!%(t-) +%(-t+) =!%(t-) AB OP M 0

171 대단원마무리 Level f()- 0 = - f()= f( f())- f( f())- f()- = [ ] - f()- - =_ =4 0 ++a -3a+3=0 D D =-(a -3a+3)=-(a-)(a-) 4 D <0a< a> 4 f(a)=0 D >0<a< 4 f(a)= D =0a= a= 4 f(a)= f(a) a= a= +=3 03 =0, = f()-f()- { f()-}{ f()-} f()=, +0 f()=, f(0)= { f()-}{ f()-}=0_(-)=0 +0 { f()-}{ f()-}=_0=0-0 { f(0)-}{ f(0)-}=0 { f()-}{ f()-} = f()=, f()=, f()=0 { f()-}{ f()-}=0_(-)=0 { f()-}{ f()-}=0_(-)=0 { f()-}{ f()-}=(-)_(-)= { f()-}{ f()-}+{ f()-}{ f()-} { f()-}{ f()-} = -, { f()-}{ f()-} f()= -0-0 =0 -, f() +0 f( f())= f(t)= f( f(-))=f(0)= f( f()) =- 04 OA +OB -AB cos 60 = OA OB (+) +(+) -(+) ;!;= (+)(+) 3---=0 = - - f() + 3- =;3!; t AB AB C O D AB D A F E O EDB= ABD AD =CD ABD= DBC EDB= DBC CDE= EBC CDB= CDE+ EDB= EBC+ DBC= EBD DB CD =EB CD =AD =EB CBD EDB SAS DE =BC = D AB F OF = AD -AF =DF =OD -OF -{- } =-{ } =- = - = ( +)= {;!;} = f() = = E B

172 f { {;!;}k } =f { {;!;} }=f() S «= (-) k+ {;!;}k <;3!; S «=;3!; f { (-) k+ {;!;}k }= f()=3 S «= k= k= k= + k= = ;3!;-0 (-) k+ {;!;}k >;3!; S «=;3!; f { (-) k+ {;!;}k }= f()=5 f { (-) k+ {;!;}k }+ f{ (-) k+ {;!;}k } f { (-) k+ {;!;}k } + k= k= k= ;3!;+0 + k= 0 f '(-)= = = (h -h+3) =3 h 0 h 0 h 0 f(-+h)-f(-) h h -h +3h h f(+)-3 0 =4 0-0, {f(+)-3}=0 f()=3 +=t f '()=8 h 0 a=;4#; f(+)-3 - = = t t f(t)-3 t -t f(t)-f() (t-)t f(t)-f() = t _ t ;t!; t- =;!; f '()=4 f(+ah)-f() f(+ah)-f() = _a h h 0 ah =af '() =8a=6 03 g(0)=4 h 0 = h 0 f(a+h)-f(a)-g(h)+4 h f(a+h)-f(a) = h 0 - h =f '(a)-g'(0)=6 f '(a)=g'(0)+6=0 f '(a)=0 f(a+h)-f(a)-{g(h)-g(0)} h h 0 g(0+h)-g(0) h 0

173 04 f()= h +0 h -0 = = = = = = = =- f(0+h)-f(0) f(0+h)-f(0) + h +0 h h -0 h f() =0 f()= h 0 = = = = h =0 f '(0)=0 f() =0 f()=+ h +0 h -0 f(0+h)-f(0) h f(0+h)-f(0) h f(0+h)-f(0) h f(0+h)-f(0) h f(0+h)-f(0) h = = = = = h +0 h +0 h +0 h -0 h -0 h -0 h 0 h 0 h 0 h 0 h +0 h +0 h +0 h +0 = h -0 = h -0 = h -0 f(h)-0 h h h f(h)-0 h h h -h h f(h)-0 h f(h) h h h h f(h)-0 h h+ h h h+h h f(h)-0 h h+ h h h-h h =0 f(0+h)-f(0) f(0+h)-f(0) + h +0 h h -0 h f() =0 =0 h h h h 05 f(0)=0 = = 0 g () =g(0) g() =0 =0 f '(0)=0 f() =0 f()= (+0) f(0)=0, g()=[ =0 0 (=0) g()-g(0) = = = g()-g(0) - = = = g()-g(0) g()-g(0) g() =0 g()=h() = = = g () =g(0) =0 h'(0)=0 h()=g() =0 =0 06 f()=;3!; -8+ f '()=;3!;_3-8= -8 f '(3)=9-8= h =_ h 0 =f '(3) = = f()-f(0) -0 h()-h(0) -0 f(3+h)-f(3) h 07 f()=- +4 f '()=-3 +4 f(3+h)-f(3) h f '()= g()= f() g()-0 g(0) -0 g() 3

174 g'()=4-3 g'()=, f()=3=g() h 0 = =;!; f(+h)-f() g(-h)-g() =;!; [ h 0 + h 0 ] h -h =;!; {f '()+g'()} = h 0 f(+h)-g(-h) h h 0 f(+h)-f()+g()-g(-h) h { f(+h)-f()}-{ g(-h)-g()} h 08 f()= f '()= f '()=3+6-4=5 ;!;=h h +0 g(-)-4 = -=t - g(-)-4 g(t)-4 = = - t 0 t t { g(t)-4}=0 t 0 g(0)=4 g(t)-4 g(t)-g(0) = t 0 t t 0 t =g'(0)= F()=f()g() F(0)=f(0)g(0)=4 f(0)= f()g()-4 F()-F(0) = 0 0 =F'(0) F'()=f '()g()+f()g'() F'(0)=f '(0)g(0)+f(0)g'(0) F'(0)=6_4+_ f(0)=, f '(0)=6 F'(0)=6 6 [f{+;#;}-f{-;!;}] = h +0 = h +0 f(+3h)-f() f(-h)-f() =3_ + h +0 3h h +0 -h f() 3f '()+f '()=4f '()=4 5=0 09 f()=( +)( -+) f '()=( -+)+( +)(-) f '()= f '()= (, ) f '()=4-3+4-=4 0 g()=(3 -)f() g()=(3 -)f()=f()=6 f()=3 g'()=(6-)f()+(3 -)f'() g'()=5f()+f'() =5 3+f '() f '()=- f(+3h)-f(-h) h f(+3h)-f()-{ f(-h)-f()} h 0 f()= +a+b f '()=+a h 0 =3 h f(0)=b=0 f(h) f(h)-f(0) h 0 = =3 h h 0 h f '(0)=3 f '(0)= 0+a=3 a=3 f()= +3, f '()=+3 f '()=5, f()=4 f '()+f()=5+4=9 3 f()= +p+q f '()=+p f(h) h f() - = f()=0 f()=+p+q=0 f() f()-f() = =f '()= f '()=+p=-4 p=-6, q=5 4

175 f()= -6+5, f '()=-6 h 0 = f(a+h)-f(a) = h 0 + h =f '(a) =(a-6) =4a- = a=6 f()- 4 =- +-3 f()- =- +a+b a, b f()= - +a+b f '()=3-4+a =4 0 0 f()=0 f()=-+a+b=0 f() f()-f(), = =f '()=4 - - f '()=3-4+a=4 a=5, b=-4 f()= , f'()=3-4+5 f(3)+f'(3)=0+0=40 =- f()- =- +a+b a, b f()= - +a+b 40 =4 0 0 f()=0 f()=-+a+b=0, b=-a+ f()= - +a-a+ f()=(-)( -+a-) h 0 f(a+h)-f(a-h) h f() - f()- +-3 f() - f(a+h)-f(a)- f(a-h)+f(a) h h 0 f() = ( -+a-) - f(a-h)-f(a) -h =-+a-=4 a=5, b=-4 f()= , f'()=3-4+5 f(3)+f'(3)=0+0=40 5 =0 a=4 f()= f()=f(0) =0 b=3 a+b=7 = = (h+3) =3 = (h +b) =b +3+a (<0) f()=[ +b+4 (æ0) +3 (<0) f '()=[ 6 +b (>0) =0 =0 a=4 f()= f()=f(0) =0 b=3 a+b=7 f '()= f '() 6 f() =- --0 f()= a=--b+c f()=f(-) f() = -0 f()= f()=f() +b+c=- f() = h -0-0 h -0 h f(h)-f(0) = h h -0 f(h)-f(0) = h h h -0 h -0 h +0 f(+h)-f() = h h -0 h +3h+4-4 h h +3h h h +bh+4-4 h (+h) +b(+h)+c-(-) h h +3h +(3+b)h = h -0 h =3+b 7 5

176 f(+h)-f() --(-) = =0 h +0 h h +0 h 3+b=0 a=3, b=-3, c= ( 3 (<-) f()= -3+ (- <) 9 - (æ) f(-+h)-f(-) 3-3 = =0, h -0 h h -0 h h +0 = h +0 = h +0 =0 f() =- f() abc=-9 f() =- f()= f()=f(-) a=--b+c f() = f()= f()=f() b+c=- 0 (<- >), f '()=[ 3 +b (-<<) f() =- -+0 f '()= f '() 3+b=0, b=-3 f '()= f '() f() = a=3, b=-3, c= abc=-9 ( - (<0) 7 g()= f()= 0 (=0) 9 (>0) -3 (<0) g'()=[ 3 (>0) g'(-)=-3 (-) =-3 g'()=3 =3 h +0 f(-+h)-f(-) h (-+h) -3(-+h)+-3 h h -3h h g(0+h)-g(0) = h h +0 h h -0 h -0 = h =0 = (-h ) =0 g(0+h)-g(0) g'(0)= h 0 =0 h g'(-)+g'(0)+g'()=(-3)+0+3=0 8 f(+)=f()+f()-6- =0 f(+0)=f()+f(0)- f(0)= f(h)-f(0) f(h)- f '(0)= h 0 = h 0 =3 h h f '()= f '()= h 0 h 0 h +0 g(0+h)-g(0) = h h -0 h -0 f(+h)-f() h f()+f(h)-6h--f() h f(h)- f '()= h 0 [ -6] h f '()=f '(0)-6 f '()=3-6 f'{-;!;}=3-6 {-;!;}=6 -h h 6

177 =- l, l l (0, ) l --= d= = =!% +(-) d =8 8 0 f()= -5+ f '()= A, B =- -0 (t, t -5t+) f '(t)=4t -5=- t= f()=-3 +3=-(-) =-- a-b=--(-)= 04 f()= +a, g()=b -4 f '()=3 +a, g'()=b = f()=g(), f '()=g'() f()=g() 8+a=4b-4 a-b=-6 f '()=g'() +a=4b a-4b=- a=0, b=3 a +b =0+3 =9 9 0 f()= - f '()=3 - (t, t -t)=t f '(t)=3t - -(t -t)=(3t -)(-t) (, 3) 3-(t -t)=(3t -)(-t) t -3t +5=0 (t+)(t -5t+5)=0 t=- l =+, -, S S=;!; = 05 f()= -0-7 f '()=3-0 f '(-)=3 (-) -0= =f() (-, -5) +5=(+) =- g()= g'()= g()= (a, a ) -a =a(-a) =a-a =- a=, -a =- a= 03 f()=- +4 f '()=-3 +4 (t, -t +4t) f '(t)=-3t +4= t = t=- t= (, 3) l l -3=- =+ (-, -3) l l +3=+ 06 f()= f '()=3 f()= P(a, a ) -a =3a (-a), =3a -a g()= -4 g'()=3 g()= -4 Q(b, b -4) -(b -4)=3b (-b), =3b -b -4 3a =3b -a =-b -4 a -b =0, (a-b)(a+b)=0 7

178 a=-b ( a+b) f()=-3+a=3 a=5 a=, b=- f(-)=-+3+a=+5=7 a-b=-(-)= 7 07 f()=a +b (a+0) f '()=3a +b f() -, f '()=3a +bæ0 3a +b=0 D a>0, D=-ab 0 a>0, bæ0 f()=a+b= (a, b) m=!% + = m =8 08 f()=;!; -4k + f '()= -k +=( -6k+) <0, f() f '() 0-6k+æ0 >0, f() f '()æ0-6k+æ0 8, -6k+æ0-6k+=0 D D =9k - 0, (3k-)(3k+) 0 4 -;3!; k ;3!; b-a b O a 0 f()=;3!; -a +(a+5)+ f '()= -a+a+5 f() f '()=0 -a+a+5=0 D D>0 D 4 =a -(a+5)=(a-5)(a+3)>0 a<-3 a>5 a 6 f()= f '()= -4 +=(-) f '()=0 =0 = f() f '() f() f '()=0 =0 = f '()=0 <0 f '()<0 f() (-, 0) f() =0 = f '() f() ;3!;-{-;3!;}=;3@; =f '() 09 f()= -3+a f '()=3-3=3(-)(+) f '()=0 =- = f() - f '() f() f() =-, = f()=3 a c d O e» f f '(k)=0, =k f '() f() =k =d f '() (+) (-), =a =f =b f '() (-) (+), f() f '(k) =k f '() f() =k b 8

179 f'(g) =g f '() (+) (-), f() 3 0m+=0_+3=3 3 3 f '()=0 =- =0 = =f '() <-, f '()>0, f '()<0 f() -<<0, f '()<0, f '()>0 f() 0<<, f '()<0, f '()<0 f() >, f '()>0, f '()>0 f() f() - 0 f '() f() f() =- f() =0 (0, ) f '()<0 f() 4 f()= f '()= =-3(-) f '()=-3(-) 0 f() -, -, a f(a) f(a)=-a +3a -3a=-9 (a-3)(a +3)=0 a=3 5 f()=a -3a +b f '()=3a -6a=3a(-) f '()=0 =0 = 3 f() f()=b-a, f()=b-4a, f(3)=b a>0 b, b-4a b=5, b-4a=4 4a= a=;4!; 6 f()= =t 0, 4 t 4, g(t)=t -3t +3, t 4 g'(t)=3t -6t=3t(t-) g'(t)=0 t=0 t=, 4 g(t) t 4 g'(t) g(t) 9 g()=, g()=-, g(4)=9 M=9, m=- M+m=9+(-)=8 8 7 r, h r+h=4 h=4-r f(r) f(r)=pr h=pr (4-r)=-pr +4pr f '(r)=-3pr +48pr=-3pr(r-6) f '(r)=0 r=0 r=6 0<r<4 f(r) r (0) 6 (4) f '(r) f(r) f(r) r= O(0, 0), P(t, -t -3t+9), Q(t, 0) OPQ S(t) 0<t<;#; -t -3t+9>0 S(t)=;!; t(-t -3t+9)=-;!; (t +3t -9t) f '() f() b-a f() = b S'(t)=-;!; (3t +6t-9)=-;#; (t+3)(t-) S'(t)=0 t=-3 t= 0<t<;#; S(t) 9

180 t (0) {;#;} S'(t) S(t) S(t) t= S(t) S()=-;!; (+3-9)=;%; p+q=+5=7 7 9 = -6+9 '=-6 (a, b)= -6+9 (a, a -6a+9) -(a -6a+9)=(a-3)(-a) =(a-3)-a +9, = `_6+9 A, B a+3 OA =, OB =-a +9 B (a,`b) OAB S(a) O A S(a)=;4!; (a+3)(-a +9) S'(a)=;4!; (-3a -6a+9) S'(a)=-;4#; (a+3)(a-) 0 f()= -a +a+ f '()=6 -a+a f() f '()æ0 f '()=0 DD 0 D 4 05 =a -a 0 0 a a 0,,,,, f() = f() f '()=3-3=3(+)(-) f '()=0 =- = f() S'(a)=0 a=-3 a= 0<a<3 S(a) a (0) (3) S'(a) S(a) S(a) a= a=, b=-6+9=4 a+b=+4=5 5 - f '() f() f() =-, = f(-)=k+= k=;!; f()=k-3= k=;%; k;!;+;%;= g()=f()-f(a) g'()=f '() g'(a)=f '(a)=0, g'() f '() =a f() =a g() =a g() =a g(a)=f(a)-f(a)=0 g() =»() =»() a a 0

181 =g() >a g()>0 >a g()>0 04 f(-)=f() f()= +a +b f '()=8 +a = f '()=8+a=0 a=-4 f '()=8-8=8(+)(-) f '()=0 =- =0 = f() = =- =0 f()= -4 +b f(0)-f()=b-(-4+b)= 05 - f()=- +a +b +c+d f '()=-4 +3a +b+c f(+)=f(-) f() =, = =0 7 =f(), = f '()=-4 +3a +b+c f '()=-4(-)(-) f '()= O a=4, b=-4, c=0 f()= d f()= d=7 d=7 f()= = = -3+4=m -3+4=m, -3+4-m=0 f()= -3+4-m f() _<0 f '()=3-3=3(-)(+) f '()=0 =- = f() - f '() f() f() =- 6-m, = -m f(-)f()<0 (6-m)(-m)<0 <m<6 m 3, 4, 5 07 (log ) -6log +a=0 (a>0), (log ) -log +a=0 log =t f(t)=t -t+a=0 f(t) f(t) _>0 f '(t)=3t -=3(t+)(t-) f '(t)=0 t=- t= f(t) t - f'(t) f(t) f(-)f()=(6+a)(-6+a)>0 a<-8 a>8 a 9 08 f()=;4!; - +a+3 f '()= -3 +a f() f '()=0 g()= -3 +a g()=0 g() _<0 g'()=3-6=3(-) g'()=0 =0 = g() 0 g'() g() g(0)g()=a(a-4)<0 0<a<4 a++3=6 6

182 09 f() =f () ;; 8ª;; _ O =f() a O b = f(0)>0 -+a>0 a> _ =_ f()<0 f() -=0 f() = f()= f()=- f()=, f()=- 3 0 ;3!; --+a=0 a=-;3!; ++ f()=-;3!; ++ f '()=- +=-(-)(+) f '()=0 =- = f() - f '() ;3!;--+a<0 a<;3%; <a<;3%; f()= +3 +a f '()=6 +6=6(+) f '()=0 =0 =- <0 f() - (0) f '() f() <0 f() =- f() f(-) 0 f(-)=-+3+a=a+ 0 a - a - f() ;3!; =f() =a a <a<;3%; ;3%; =f() ;3%; _ O ;3!; =a f()= +4-k f '()=3 +4 f '()=3 +4>0 f() -, > f()>0 f()æ0 f()=6-kæ0 k 8 k 8 8 f()=;3!; --+a f '()= -=(-)(+) f '()=0 =- = f() =- = f() =f() 3 si =t (- t ) (si ) +3a-=t +3a- (si ) +3a-æ0 - t f(t)=t +3a-æ0 f '(t)=6t æ0 - t f(t)æf(-) - t f(t)æ0 f(t) f(-)=3a-4æ0 aæ;3$;

183 a ;3$; 4 t v(t), a(t) d v(t)= =3t -6t+ dt dv a(t)= =6t-6 dt v(t)=3t -6t+=0 3t -6t-9=0 t -t-3=0, (t+)(t-3)=0 tæ0 t=3 t=3 a(3)=6_3-6= 5 P P 0 Pt v(t) d v(t)= =3t -8t+4=3(t-)(t-4) dt v(t)=0 t= t=4 P t=4 P = =6 6 6 t P, Q f(t)=t -6t+5, g(t)=t -t -tp, Q v P (t), v Q (t)v P (t)=t-6=(t-3) v Q (t)=3t -t-=(3t+)(t-) t=0v P (0)= 0-6=-6 v Q (t)=(3t+)(t-) t 3t+>0 t= v Q Q P, Q v P (t)>0, v Q (t)<0 v P (t)<0, v Q (t)>0 v P (t)>0, v Q (t)<0 (t-3)>0, (3t+)(t-)<0 t v P (t)<0, v Q (t)>0 (t-3)<0, (3t+)(t-)>0 <t<3, <t<3 P, Q 7 cm t (+t) cm V(t) V(t)=;3$; p(+t) =;3$; p(t +6t +t+8) V'(t)=;3$;p(3t +t+) t= V'()=;3$;p(3++)=36p(cm / ) a=36 8 t 36 (0+0.t) cm, (8+0.4t) cm V(t) V(t)=p(0+0.t) (8+0.4t) V'(t)=(0+0.t)_0._(8+0.4t)p +(0+0.t) _0.4_p V'(t)=0.4(0+0.t)(8+0.4t+0+0.t)p V'(t)=0.4(0+0.t)(8+0.6t)p V'(0)=0.4_4_30p=68pcm 9 AB =0 cm Pcm tap, PB AP =t cm, PB =(0-t) cm 0<t<0 AP, PB pt +p(0-t) S=p 0 -{pt +p(0-t) } S=p(00-t -00+0t-t ) S=p(0t-t ) ds dt =p(0-4t) t=s p(0-4 )=p cm a= 3

184 대단원마무리 Level f()=(-)( -+3)+ f '()=(-)'( -+3)+(-)( -+3)' f '()=( -+3)+(-)(4-) f '()=(-+3)+0=4 0 =a f '(a)=ta ;4#;p=- h 0 f(a-h)-f(a) = h 0 [-;3@;_ ] -h =-;3@; f(a-h)-f(a) 3h h 0 =-;3@; f '(a)=;3@; f(a-h)-f(a) -h =-;!; f'{-;!;}=;4#;-a+b=;4!;(3-4a+4b)<0 3-4a+4b<0,, 05 f()= -a +3a+ f '()=3 -a+3a f() f '()=3 -a+3a=0 f '()=0 DD>0 D 4 =a -9a>0, a(a-9)>0 a<0 a>9 a f() f '() (-) f()f '() f() = f()= +a+b f '()=+a f()f '()=( +a+b)(+a) f()f '()= +3a +(b+a )+ab f()f '()= a=-3, b+a =5, ab=- a=-, b= f()= -+={-;!;} +;4&; f() =;!; ;4&; 06 +;3$; +a> +4 +;3$; - -4+a>0 h()= +;3$; - -4+a h()>0 h'()= =4(+) (-) h'()=0 =- = h() - h'() h() a+;3%; h() = h() 04 f()= +a +b+c f '()=3 +a+b f(), f '()=3 +a+b=0a, b a<b a<-, 0<b< =f '() _ a a O b a+b=- <0, ab=;3b;<0 3 a>0, b<0 h()=+;3$;--4+a=-: 3 :+a h()>0 -: 3 :+a>0 a>: 3 : 07 P, Qt f(t)=;3!;t +t -3t, g(t)=t + P, Q v P (t), v Q (t) 4

185 v P (t)=f'(t)=t +t-3, v Q (t)=g'(t)=t, P, Q a P (t), a Q (t) a P (t)=v P '(t)=t+, a Q (t)=v Q '(t)= v P (t)=v Q (t) t +t-3=4t t -t-3=0, (t-3)(t+)=0 t=3 ( tæ0) a P (3)-a Q (3) = 8- =6 08 tab +t, BC -0.5t(0<t<4) ABC=60Á ABC S(t) S(t)=;!;(+t)(-0.5t)si 60Á S(t)= 3 (-0.5t +6t+44) 4 S'(t)= 3 (-t+6) 4 t= ABC S'()= 3 (-+6)=3 4 6 대단원마무리 Level f() g(t),, 3 g(t)t g(t)t g(t) f()(-, ) f '()=3-6a+3(a+)æ0 f '()=0 D D =9a -9(a+) 0 4 a -a- 0 (a-)(a+) 0 - a a -, 0,, 4 f() 0 = 0-0 f()=0 ( (-)(3-) (+0 +) f()= (=0) 9 (=) f() = f '() f() 0 t=f() f( f()) f(t) = = f() t 0 t f( f()) f( f()) f() = [ ] - f() - f(t) f() = t 0 t - = 03 f() + f()=(+)f () g() - g()=(-)g () (-)f()=(+)g() f ()=g () h()=(+)g() 5

186 g() - =3 g()=0g'()=3 h'()=g()+(+)g'() h'()=g()+g'()=6 04 f()= f()=(-) Q()+a+b a, b) f()=- a+b=- f '()=00-4+=(-)Q()+(-) Q'()+a f '()=97 a=97 b=-99 f()=(-) Q() f(0)=- Q(0)=97 f '()=(-)Q()+(-) Q'()+97 f '(0)= Q'(0)=98 06 g'()=f '()f() g'()<0 f()f '()<0 f()<0, f '()>0 0<<a f()>0, f '()<0 -b<<-a b<<c -b<<-a 0<<a b<<c 05 g()= f() f()= f()= f()=0 f '()= f '()= f '()= f() (-)g() g() f()=0 f '()=g() g() f '()= ( g()= f()-f() - f() - (<0) + (0 <) (æ) ( - (<0) f()= (+)(-) (0 <) 9 (-) (æ) f()-f(0) --(-) = = -0 f()-f(0) (-)(+)-(-) = =0 +0 f() =0 6

187 P(t f(t)) =f'(t)(-t)+f(t) =f'(t)-tf'(t)+f(t) f'(t)=3t +4t+g(t)=-tf'(t)+f(t) f(t)=: (3t +4t+)dt f(t)=t +t +t+c C g(t)=-t -t +C f() = g() =-;!; + ++C - - +C = +f'(0)+c C f(0)=- C=- f()= +f'(0)- f()=+f'(0)- f'(0)=f() f'(0)=0 f()= - f() f ( ) f'()=3 +f'(0)=0 f'(0)<0 3 +f'(0)=0 a (a>0) -a =-a -a -f'(0)a-=a a +f'(0)a- (-a -f'(0)a-)+(a +f'(0)a-)=- 0 f'()+g'()=3 + f()+g()=: (3 +)d 04 f()=(_) ` f()+g()= ++C C f()=-g()+ ++C g()+f'()= -5 O g()= -f'()-5 f()=-g()+ ++C = - +{f'()+}+c+5 :_! (-) d f'()=a f'()=3 -+a+ f'()=+a=a =:_0! {-(-) }~d+:) (-) d =[-;4!; +;3@; -;!; ]0_!+[;4!; -;3@; +;!; ]) a=- f'()=3 --3 g()= +4-5 f'()+g()=5+7= = -{-;4!;-;3@;-;!;}+{;4!;-;3@;+;!;} =;#; 03 f(+)=f()+f()+3(+)+ =0=0 f(0)=- f'()= f'()= f'()=3 +f'(0) h 0 h 0 f(+h)-f() h f(h)+3h(+h)+ h f()=: {3 +f'(0)}~d 05 (ab) f() f'()<0 (bc) f() f'()>0 :Ac f'() d=:ab {- f'()}d+:bc f'()d =-{ f(b)-f(a)}+{ f(c)-f(b)} =f(a)+f(c)-f(b) =3-_3 =7 7 7

188 06 0 < f()=:)/ (-t)dt+:? (t-)dt f()=[t-;!;t ]/)+[;!;t -t]? f()={ -;!; }+{;!;-}-{;!; - } f()= -+;!; æ f()=:) (-t)dt f()=[t-;!;t ]) f()=-;!; :) f()d=:) { -+;!;} d+:! {-;!;} d :) f()d=[;3!; -;!; +;!;])+[;!; -;!;]! :) f()d={;3!;-;!;+;!;}+(-)-{;!;-;!;} :) f()d=;3$; 07 f(t)=t +at-f'(t)= f(t) :@/ (t +at-)dt= :@/ f(t)dt - - f()=8+a-=5 a=- = =F'() =f() O F()-F() - O = t_ = t_ t t = =(+k) =4+4k =6 k=3 f()= +3 g()= +6-7 f()-g(0)=4-(-7)= f()= +a+b f'()=+a g'()=f()f'() =( +a+b)(+a) =4 +6a +(a +b)+ab g()=0 g()= +a +(a +b) +ab -{+a+(a +b)+ab} a=0 g()= +b -(+b) g'()=4 +4b g() g()-g() = g()=0 - - =g'() =4+4b =6 b=3 f()= +3 g()= +6-7 f()-g(0)=4-(-7)= 09 :_0@ f(+)d =:_! (-) f()d (-)(+)( +k+) - =:_0! (-) (+)d+:) (-) (-+)d 08 { f(t)f(t)}'=f'(t)f(t) g()=:!/ f'(t)f(t)dt g()=[{ f(t)} ] l g()={ f()} -{ f()} g(-)=g() f()= +k k g()=( +k) -(+k) g() = - ( +k) -(+k) - =[;4!; -;3!; -;!; +]0_!+[-;4!; + -;#; +]) ={-;4!;-;3!;+;!;+}+{-;4!;+-;#;+} =;6&; :_0@ f(+)d =:_-@ (+)d+:_0! (-)d =[;4!; +;3@; ]-_@+[-;4!; ]0_! 8

189 3 :}+;4!; =;6&; B=:) f()d=3 :) f()d=:) f()d=6 0 :_@ f()d =:_0@ f()d +:) f()d =:_0@ f()d +:_0@ f(+)d =:_0@ f()d+:_0@ { f()+3 ++} d =:_0@ f()d+:_0@ (3 ++)d =:_0@ f()d +[ + +]0_@ =:_0@ f()d +6 =:_0@ f()d +6 :_0@ f()d=-;%; 3 f()=p+q p+0 :_! g()d =:_! (-a)(-b)f()d =:_! (-a)(-b)(p+q)d =:_! { p -(ap+bp-q) +(abp-aq-bq)+abq} d =:) {- (ap+bp-q) +abq} d =[-;3!;(ap+bp-q) +abq]) =-;3@;(ap+bp-q)+abq=0 -;3@;(ap+bp-q)+abq=0 -;3!;(a+b)p+{ab+;3!;}q=0 pq f(+)=f(-) f(+4)=f() =f() 4 :_@ f()d=3 :N 4+ f()d=3 :@4 f()d= :) f()d=:)4 f()d-:@4 f()d =3- = : f()d=: f()d+: f()d : f()d+: f()d =3_3+:) f()d =9+ = a+b=0ab=-;3!; a +b =(a+b) -ab=;3@; 4 ;!; ;K+! {+;K;}4 = ;!; ;K+! {;K;}4 [;!; ;K+! {+;K;}4 ]=:! d=[;;5;; fi ]!=: 5 : [;!; ;K+! {;K;}4 ]=:) d=[;;5;; fi ])=;5!; ;!; ;K+! {+;K;}4 ;!; ;K+! {;K;}4 (+) +(+) +(+3) ++(+) =3 3 f()=a(-) +b = :_! f()d=a:) f()d=b :_! f()d=:!3 f()d A=A+B=5 5 g()= f{- k} k= 7 g()=-:?0 f(t)dt 7 g()=:)/ f(t)dt g'()=f() 9

190 g()=:) f(t)dt g()=:) (3t -4t-)dt =;4%;-0 =;4%; g()=[t -t -t]) g()=--0 g()=- g()+ g()-g() = - - =g'() =f() k 8 f( )=a = A =;!;( + - ){ f( + )-f( )} A =;!;( - ) a ( - ) =- 6 a«b«+ =:N a«d_: + a«6 a«b«+ =:N + d_:n + d 6 a«b«+ =[;!; ]N + _[;!; ]N + 6 a«b«+ =4(+) a =b = a«b«=4 (a b ) = 6k fi k= fi k= k = 6{ } 4 k= =6:) d fi =6[ 5 ]) d A =;A;( - ) ( + ) k+ A =;A; (k+)a A = - - (k+)a a S()= A = = k=0 k=0 S()S(+) = a a = = + = a = 8 a 8 a =6 a 4 = = a=4 a>0 (+) =6{;5!;-0} =: 5 : 7 =;K; f( )+f( ) ;!;[ ] k= 3 =;3!;[ f( - );!;+ f( );!;] k= k- k =;3!;[ f{ };!;+ f{ };!;] k= k= - k k =;3!;[ f{ };!;+ f{ };!;] k=0 k= =;3!;[:) f()d+:) f()d] =:) f()d =:) ( +)d =[;4!; +]) k= 30

191 ='ƒ+ = - S S=:) - d _ O = / + ß = S=-[{;4!;+;3!;-}-0] S=;6%; 03 f'()=a(+)(-)=a( -) a>0 f()=: f'()d=a{ - }+C C 4 f() a=4 f()= - +C f() =-= 0 f(-)=f()=-+c=0 C= f()= - + =f() =f() S=:) (- )d+:! ( -)d S=[- ])+[ -]! 3 3 _ O S=;3@;+;3$;= :_! ( - +)d=:) ( - +)d 0 f()=(+)(-) =f() =f() :_! ( - +)d=[ -;3@; +]) :_! ( - +)d={;5!;-;3@;+} :_! ( - +)d=;!5^; fi 5 _ O =f( ) æ0 =f( ) =f() <0 =f( ) =f(-) >0 =f() =f( ) =f( ) 04 = '= = ` () -=(-) =- :) { -(-)} d=:) ( -+)d :) { -(-)} d=[ - +]) 3 :) { -(-)} d={;3!;-+}-0 O _ = O :) { -(-)} d=;3!; S S=-:) ( + -)d S=-[ + - ]) f()= +4 f'()=3 3

192 +4=3-3 +4=0 g()= -3 +4g(-)=0 (+)( -4+4)=0 (+)(-) =0 =- = f '()=3 4 :_! - d=4:) (- )d :_! - d=4[ - ]) 4 :_! - d=4[{;!;-;4!;}-0] :_! - d= 07 = - = ` f()= `+4 O O A B :_! {( +4)-3 } d=:_! ( -3 +4)d :_! {( +4)-3 } d=[ - +4]_! :_! {( +4)-3 } d=(4-8+8)-{;4!;+-4} 4 :_! {( +4)-3 } d=4+: 4 :=: 4 : =k A, B A, B :)k ( -)d=[ - ]k) 3 k k :)k ( -)d= - 3 :)k ( -)d= k 3 k=;#; ( k>) {k-;#;}=0 06 f()= +a +a f() f'()=3 +a+a f'()æ0 f'()=0 D D =a -3a 0 4 a(a-3) 0 0 a 3 a 0 f()= f()= =f ()f()= =f () = = = _ O _ = = =f` `() 08 =m =_ A B O = A, B :) {(- )-m} d=:) {(-m)- } d -m :) {(- )-m} d=[ - ]) 4 -m :) {(- )-m} d= -;4!;=0 m=;!; = = =(+)(-)=0 =- =0 = 09 [0 a] [a b] =f() AB[0 b] =F()=G() 3

193 A+B A A_B O a =G() =F() b v P (t)æ0 P v Q (t)=t(t-) Q 0<t<P t>p PQ s P (t)s Q (t) =F() 3 A=3 =G()-F() 4 B B=4 B= [0 b] =f() A+B=3+=5 0 a(t) 3 a(t)=v'(t)=t-=3 t= t= P t t 0+:) (t -t)dt=[ - ])=;3*;-=;3@; 3 v(t)=3(t -6t+5)=3(t-)(t-5) v(t)=0 t= t=5 s(t) s(t)=:)t v(t)dt s(t)=:)t (3t -8t+5)dt s(t)=[t -9t +5t]t) s(t)=t -9t +5t s()=7s(5)=-5s(6)=-8 P t=5 t=0 t=5 P s s=:)5 v(t) dt s P (t)=0+:)t tdt=[;!;t ]t)=;!;t t t t t s Q (t)=0+:)t (t -t)dt=[ - ]t)= s P (t)=s Q (t) t t t = - 3 ;3!;t (t-3)=0 t=0 t=3 PQ t=3 PQ t=3 t 0<t 3 PQ f(t) t t t t f(t)=s P (t)-s Q (t)= -{ - }=- +t 3 3 f'(t)=-t +t=-t(t-) f(t) t= f()=;3$; 3 v(t)=a(t-)(t-) a>0 v(0)= a= v(t)=(t-)(t-)=t -3t+ t= P +:) v(t)dt=+:) (t -3t+)dt t +:) v(t)dt=+[ -;#;t +t]) 3 +:) v(t)dt=+{;3*;-6+4} +:) v(t)dt=;3%; s=:) v(t)dt+:!5 {-v(t)} dt s=[s(t)])-[s(t)]5! s=s()-s(0)-{s(5)-s()} s=s()-s(5) s=_7-(-5) s=39 4 ABC S S S v(t) A O a B b c C t 33

194 = 9 :)c v(t)dt=s -S +S :Ab v(t) dt=s :)c v(t)dt=:ab v(t) dt S =S +S P 3 :Ab v(t) dt=s =3 Pt=c :)c v(t) dt=s +S +S =3S =9 9 대단원마무리 Level :_! (+)(+) d-:_! (+)(-) d =:_! (+){(+) -(-) } d =:_! 8(+)d =8:_! ( +)d =8:_! d 5 ABCD S S S S :)b {v P (t)-v Q (t)} dt=0 v P (t)v Q (t) S =S t P Q s P (t) s Q (t) t=b v(t) v (t) vœ(t) A C B D a b t s P (b)=:)b v P (t)dt=s +S +S s Q (b)=:)b v Q (t)dt=s +S +S O =6:) d =6[ ]) 3 =: 3 : 0 :) { f'()+3 }d=[ f()+ ]) ={ f()+}-{ f(0)+0} = f()-f(0)+ = f() f(0)= S =S t=bp, Q 0 t a P, Q a t b P, Q t=ap, Q P, Q t=b 03 f(t)=(t+) 0 F'(t)=f(t) :!/ (t+) 0 dt= :!/ f(t)dt - - = _ :!/ f(t)dt + - =;!; =;!;F'() F()-F() - =;!;f() =;!;_ 0 04 f{;k;};@;= f{;k;};!;=:) f()d k= :) f()d=:)a f() d k= 34

195 f()=- (-) 0 f()æ0æ f() 0 :)3 v(t) dt=:) v(t)dt :)3 v(t) dt=:) (t-)(t-3)dt :)3 v(t) dt=:) (t -4t+3)dt =_ `+ O t :)3 v(t) dt=[ -t +3t]) 3 :)3 v(t) dt=_;3$; :)a (- + )d=[- + ]a) 4 3 a a :)a (- - )d= a :)a (- - )d=- {a-;3$;}=0 4 a=;3$; ( a>) =a :)3 v(t) dt=;3*; 05 ='ß = S =:) d=[ ])=;3!; 3 = fi S =:) d=[ ])=;5!; 5 S =-(S +S )=-{;3!;+;5!;}=; 5; S ; 5; = =;8&; S +S ;3!; +;5!; 06 v(t)=(t-)(t-a) P 0 t t a tæa P t=a 0 0+:)a v(t)dt=0+:)a (t-)(t-a)dt t t 0+:)a v(t)dt=[ -(a+) +at]a) 3 a a 0+:)a v(t)dt= -(a+) +a 3 a 0+:)a v(t)dt= {a-3(a+)+6} 6 a 0+:)a v(t)dt=- (a-3)=0 6 a=3 ( a>) v(t)=(t-)(t-3) P t=0 t=3 t=0 t= 35

196 대단원마무리 Level f() f()0 f() =f() {(A)(B)}{44}{35}{6}{7} (A)(B) 657 {(A)(B)} {7} (A)=(B)=7 A;B={} s(a)= s(b)=8 (A)-(B) + s(a)-s(b) =6+7=33 O _c c f()= (-c)(+c) (c>0) c c f'()=4{- }{+ } ' ' c a= ' :)a f'()d=-4 f(a)-f(0)=-4 f(0)=0 c f(a)= f{ }=-4 ' c c f{ }=- ' 4 c =6 c= ( c>0) f()=0 c - 03 I -I =:) d + (- )(+ ) 04 I -I =:) d + 04 I -I =:) (- )d 04 I -I =;3@; I +I + =:) I +I + =:) - d d I +I + = - 5 (-) k+ k= k- =(I +I )-(I +I )+(I +I )-(I +I )+(I +I ) =I +I 0 :) s(a) s(b) d=[ s(a)+s(b)+ ]) s(a)+s(b)+ = =;3 0; s(a)+s(b)+ s(a)+s(b)=9 A'B=E 7 8 s(a'b)= =8 s(a'b)=s(a)+s(b)-s(a;b) s(a;b)= A;B={} (A)+(B)=(A'B)+(A;B)=7+=8 I=:) (A) d+:) (B) d+:_0! (A;B) d 04 f() =0, = f '()=a(-) a>0 f()=;3!;a -a +C C f(0)=3 C=3 f()=0 ;3*;a-4a+3=0 a=;4(; f()=;4#; -;4(; +3 :) f()d=:) {;4#; -;4(; +3}~d I= + -;!; (A)+ (B)+ 0 I= -;!;>0 (A)(B)+9 (A)(B)< =[; 6; -;4#; +3]) =3-6+6 =3 36

197 05 ABC S S S v(t) v P (t) v Q (t) A B O a C b t :)b {v P (t)-v Q (t)} dt=:)b v Q (t) dt S +S =S +S S =S t=b :)b v P (t) dt=:)b v Q (t) dt S +S =S +S S =S S =S =S P t=b :)b v P (t) dt=s +S =S =:)a v Q (t) dt 0 t a P :)a v P (t) dt<s :)a v P (t) dt< :)a v Q (t) dt t=b :)b v P (t)dt-:)b v Q (t)dt=:)b {v P (t)-v Q (t)}dt :)b v P (t)dt-:)b v Q (t)dt=s =:)b v P (t) dt P t=b 06 PO A a Ot OA P kt k μab P c c :)a kt dt= ;K;a = AOB AB :A3 c dt= c(3-a)= A ka ka=c a= 0 A A C = C = C A C = C = C C + C =+5=36 0 C = _5 3+4-C = C = C = =5 _ 0_5=50 03 A B, C 4 C _! A C -= C - C _!_( C -)=6 4=68 B 37

198 68 C 68,, 68_3= z=0, +=9 (,, 0) 9 +9-Cª= ºCª= ºC =0 z=, ++5=9 +=4 (,, ) 4 +4-C = C = C =5 0+5=5 05 X, 4 5 C X, 3, C = C C _ C =0_35= ºC 0-r r {- } = ºC (-) r 0-3r 0-3r= r=3 0_9_8 ºC (-) = _(-) = (+ ) C r () -r ( ) r = C r -r +r (r=0,,,, ), 7 +=7 =6 C 6-r 6+r, 6+r=8 r= C 6- =5_6=40 09 (+a)fi C () a =80a d d 960 (+a)fi 30a 30a=960 a=3 (+3)fi C () 3 =80 : (+3)fi d f(3)=5,, 5 4 5, 6, 7, 8 4 f(3)=7,, 5, 6, 7, 4 7, 8 3+-C _= C _=6_= 4+=6 0 (-) C (-) =4 (+)fi (+)fi C =0 4+0=34 0 (-)(+) k- k= 38

199 =(-)_ =(-)_ (+) 0 - =_ - ={(+) 0 -}- (+) 0-0_9_8 ºC = =0 3 (+) 0 - (+) 0 0_9_8_7 ºC = =0 4_3 0-0=-90 (+) 0 - (+)- (+) 0 - (+) 0 - (+) 0 - C r =;!; ( 5 -)= - 4 A 04 C + C += - =04 - = 0 -=0 = A 7 _0_9_8 C = C = =330 4_3 5 (-) = Cº- C + C - C ++(-) C, (+) = Cº+ C + C + C ++ C (- ) 0 (++ ) 0 =(+) 0 (-) 0 (++ ) 0 =(+) 0 {(-)(++ )} 0 =(+) 0 (-, L.) 0 (+) 0 (-, L.) 0 ºC ºC (- ) =, -L00L. (+) 0 (-, L.) 0 ºC _ ºCº(- ) =, 0L., -L0L0L.+, 0L.=0 f()=, a=-00, b=0 f(a+b)=f(0)=000 3 C r = C -r 7 C r = C + C ++ C r= a k =(-) k C k, b k = C k a (-) «C = = (-) k k=0 b k=0 «C k=0 ={+(-)}+{+(-)}+ +{+(-)}+ = a a = { _a } k=0 b k=0 b = {(-) k _(-) k C k } k=0 = C k = k=0 b (a +b ) b = [ (a +b )] k=0 a k=0 a = [(-) k {(-) k C k + C k }] = { C k +(-) k C k } =( Cº+ C + C +) =_ - = k=0 k=0 C r =;!; ( C + C ++ C + C ) C r =;!; ( C + C ++ C + C ++ C + C ) C r =;!; ( Cº+ C + C ++ C + C ++ C + C + C -) 39

200 _6_6=6 a b c C = C = =; 7; 0 5!=0 A B C D C D E A B, C E D! A B, C D _ =; 5; 5! 03 6_6=6, A m (-A) =(-) A m+ =E, 0 0 A ={ }{ } A ={ } - 0 A =A A - 0 A ={ }{ } A ={ } 0 - A =-E Afl =E m+=6, (m, ) (4, ), (, 4), (6, 6) 3 m+=3, 9 (m, ) (, ), (6, 3), (4, 5) =;6!; 6 04 A, B A, B P(A'B)=P(A)+P(B) C C P(A'B)= + C C P(A'B)=; 0;+; 0; P(A'B)=;5@; 05 (a-b)(c-d)>0 (a>b c>d) (a<b c<d) a>b c>d A, a<b c<d B A, B A 9 a, b 7 c, d ªC _ C P(A)= =;4!; ªP B P(B)=;4!; A B P(A'B)=P(A)+P(B)=;4!;+;4!;=;!; 06 A B X, A C Y, 40

201 08 f 5_5_5=5, A AÇ 3_3_3=3 P(A)=-P(AÇ ) 3 P(A)=- 5 P(A)=;ª 5; C _ C _ 09 6! 6!, X A B 4 3 C _ C B, A AÇ, AÇ C _ C X;Y A, B, C 3 P(X'Y)=P(X)+P(Y)-P(X;Y) 3 3 C _ C C _ C P(X'Y)= + - AÇ C _ C _;!; C _ C _;!; C _ C _;!; _3!_3! P(X'Y)=; 0;+; 0;-; 0; P(A)=-P(AÇ ) P(X'Y)=; 0; _3!_3! P(A)=- 6! P(A)=-; 0; 07 P(A'B)=P(A)+P(B)-P(A;B)=;!; P(A)=;ª0;, P(AÇ )=P(B)+;3!; -P(A)=P(B)+;3!; P(A)+P(B)=;3@; ;3@;-P(A;B)=;!; P(A;B)=;6!; (A;B) 0 P(B A)= (A) ;!;= (A;B)=;!; (A), P(B A)= ;!;= (A;B) (A) P(A;B) P(A) P(A;B) P(A) P(A;B)=;!; P(A) (A;B)+P(A;B)=;!; {(A)+P(A)} (A;B)+P(A;B)=;!;_: 3 : (A;B)+P(A;B)=;3&; A, B A,, 3, 4, 5 3 C _ =80 4

202 A;B C _ C =30 P(B A)= (A;B) (A) P(B A)=;8#0);=;8#; P(B A)=P(BÇ A) P(A;B) P(A) = P(A;BÇ ) P(A) P(A;B)=P(A;BÇ ) P(A;B)=P(A)-P(A;B) P(A;B)=;!;_P(A), P(A)=;3!; P(A;B)=;!;_;3!;=;6!; A B A;B=u P(A;B)=0 P(A;B) P(B A)= =0 P(A) A,B A;B=A P(A;B) P(A) P(B A)= = = P(A) P(A) P(A)=;!;, P(B)=;3!;, P(A;B)=;6!; P(A;B) ;6!; P(B A)= = =;3!; P(A) ;!; P(B AÇ )= P(B AÇ )= P(AÇ ;B) P(AÇ ) ;3!;-;6!; P(B AÇ )= -;!; P(B)-P(A;B) -P(A) 4 3 X, Y. 3 A A 0 % P(X;Y)=P(X)P(Y X) P(X;Y)=;3!;_;5!; P(X;Y)=; 5; 3 B B 50 % P(XÇ ;Y)=P(XÇ )P(Y XÇ ) P(XÇ ;Y)=;3@;_;!; P(XÇ ;Y)=;3!; P(Y)=P(X;Y)+P(XÇ ;Y) ;6!; P(B AÇ )= =;3!; ;!; P(B A)+P(B AÇ )=;3!;+;3!;=;3@;+ P(Y)=; 5;+;3!; P(Y)=; 5;=;5@; 3 P(B A)+P(BÇ A)= P(B A)=P(BÇ A) P(B A)+P(BÇ A)=P(B A)+P(B A) =P(B A) = P(B A)=;!; P(A;B)=P(A)P(B A) P(A;B)=;3!;_;!; P(A;B)=;6!; 5 A, MP3 B P(A)=; 0;, P(B A)=; 0;, P(B AÇ )=; 0; P(A;B) P(A B)= P(B) P(A)P(B A) P(A B)= P(A;B)+P(AÇ ;B) P(A)P(B A) P(A B)= P(A)P(B A)+P(AÇ )P(B AÇ ) 0.7_0. P(A B)= 0.7_0.+0.3_0.6 P(A B)=

203 P(A B)=; 6; 6 A, B P(A'B)=P(A)+P(B)-P(A;B) =P(A)+P(B)-P(A)P(B), P(A)=;!;, P(A'B)=;3@; ;3@;=;!;+P(B)-;!;P(B) ;!;P(B)=;6!; P(B)=;3!; 3+5-C = C = C = P(A)= =;7 ; 6 3 P(B)=;3!; A, B P(A;B)=P(A)P(B) P(A'B)=;7 ;_;3!; P(A'B)=;&6; P(BÇ )=-P(B) P(BÇ )=-;3!; P(BÇ )=;3@; 7 ab AAÇ ab, a b BB, C _ C P(B)= =;5#; C, C P(C)=;!; B C P(A)=-P(AÇ ) P(A)=-P(B;C) P(A)=-P(B)P(C) P(A)=-;5#;_;!; P(A)=; 0; 8 ++z=8 A, w 3 B,, z '=-, '=-, z'=z- ', ', z' '+'+z'=5, (', ', z') ('+, '+, z'+) (,, z) (', ', z') (,, z) (', ', z') A, 5 B ;!; P(A'B)=P(A)+P(B) P(A'B)= C {;!;} 4 {;!;} + C {;!;} 5 {;!;} 0 P(A'B)=6_{;!;} 5 P(A'B)=; 6; 0 9 A 9=3 A 3 3 ;3!; P(A)=-P(AÇ ) P(A)=-[ Cº{;3!;} 0 {;3@;} 5 + C {;3!;} {;3@;} 4 ] fi +5 P(A)=- 3fi P(A)=-;!4!3@; P(A)=;!4#3!; 3 3A, B 3 ;3!; P(B A)= P(A;B) P(A) 43

204 P(A;B) P(B A)= P(A;B)+P(A;BÇ ) ;!;_ C {;3!;} 3 P(B A)= ;!;_ C {;3!;} 3 +;!;_ C {;3!;} 3 {;3@;} P(B A)= +4_;3@; P(B A)=; ; 대단원마무리 Level =l, =m, z=+, l,m, l+m+(+)=77 l+m+=76 l+m+=38 (,, z) 40_ C = ºC = ºC = =780 0 {+ } ' C -r { } r = C r -r-;r; ' = C r -;#;r (r=0,,,, ) -;#;r=0 r=8 C _ = C _ 0_9 Cª_ = _ 4_3 Cª_ = _495 a=, b=495 a+b= a = C + C + C ++ C =( C + C )+ C ++ C =( C + C )+ C ++ C 03 a = 03 a = = C + C = + C (+)(-) 3 a «= a«= (+)(-) 6 (+)(-) 6 (+)(-) 6 (+)(-) (+)(-) = {+;!;}{-;!;} {+;!;}{-;!;} = =8 44

205 P =7! P =4_3 3 P =5! 4_3_5! 7! =;4!@;=;7@; 대단원마무리 Level ,,, 3, 4, 5, 6, 7, 8, 9 aæbæcæd C -=74 05 a, b, cabc 3 a, b, c 3 6 -{;6$;} 3 =-; 7;=;!7(; , 3 p =;6#;_;5@;_;4!;_;3@;=;3 0; 0! C A B 7 C 5 A B 7 7!A B 78 C 5 P =8_7_6_5_4 7!_(8_7_6_5_4) =;9 9;! p =;6!;_;5@;_;4!;_=;6 0; p +p =;3 0;+;6 0;=; 0; 07 A B (A, B) A (3, ), (3, ), (3, 0) (, ), (, 0) (, 0) {;!;} 3 [-{;3@;} 3 ]+ C {;!;} {;!;}[ C {;3@;}{;3!;} +{;3!;} 3 ] + C {;!;}{;!;} _{;3!;} 3 =;8!;_;!7(;+;8#;_{;9@;+; 7;}+8#;_; 7; =; ª6;+8#;_; 7;+;#6; =; 6; p=6, q=43 p+q= X f( f())=f() t<{f() <X} f(t)=t f()=, f(3)=3, f(5)=5, f(6)=6, f(7)=7, f(0)=0 a<b f(a) f(b) f() f(4) 3, 4, 5 f(8), f(9) 7, 8, 9, 0 f(8) f(9) f() f(4) f(8), f(9) f() f(4),3 f(8), f(9) 7, 8, 9, 0 f(8) f(9) f(8)=7 f(9)=8 f(8)=9 f(9)=0 f(8), f(9) 4+-C -= C -=8 _3_8=48 04 A B (A)<(B) 45

206 5 S C + C + C + C + C Cº+ C ++ C = Cº= C, C = C º,, C = C ( Cº+ C + C + C + C + C )= C + C + C + C + C = - Cº =03 05 TA B A C P(B;C)=;ª0º0;_;0@0; P(B)=P(B;C)+P(B;CÇ ) P(B)=;ª0º0;_;0@0;+;0%0;_;ª0 0; p +p +p +p +p = {p i } p +p =p, p +p =p p +p +p +p +p =(p +p )+(p +p )+p =p +p +p =5p = p =;5!; P(C B)= ;ª0º0;_;0@0; P(C B)= ;ª0º0;_;0@0;+;0%0;_;ª0 0; P(C B)= P(C B)=;6!7*; P(B;C) P(B) p 3 (-p) -(-p) =3p-3p +p 0 k P(X=)= =k(-5- ) +5- P(X=)+P(X=)++P(X=0) =k+k(-)+k(3-)++k(40-9) =40k= k= 40 P(5 X 9) =P(X=5)+P(X=6)+P(X=7)+P(X=8)+P(X=9) = (5-4)+ (6-5)++ (9-8) = (9-4) = 0 03 P(X<)=-P(Xæ) =-{P(X=)+P(X=3)+P(X=4)} X= 3, P(X=)= C {;!;}3 ;!;=4_;8!;_;!;=;4!; X=3 P(X=3)=0 X=4 4 P(X=4)= C {;!;}4 =; 6; P(X<)=-{;4!;+; 6;}=;!6!; 46

207 04 ;6!;+b+;3!;= b=;!; E(X)=(-)_;3!;+_;6!;+a_;!;=;!;a= a=4 E(X )=(-) _;3!;+ _;6!;+4 V(X)=E(X )-{E(X)} =9- =5 5 =a+3a = 3a +a-=0 (3a-)(a+)=0 a=;3!;( a>0) E(X)=(-)_;9!;+(-)_;3!;+0_;9!;+_;3!;+4_;9!;=;9@; E(X )=(-) _;9!;+(-) _;3!;+0 _;9!;+ _;3!;+4 _;9!; E(X )=: 9 : V(X)=E(X )-{E(X)} V(X)=: 9 :-{;9@;} =: 8 º: 05 A B C P(X=0)=;!;_ 3 =;!;_;3!;=;6!; C A B C _ C C _ C P(X=)=;!;_ 3+;!;_ 3 C C =;!;_;3@;+;!;_;3@;=;3@; A B C P(X=)=;!;_ 3 =;!;_;3!;=;6!; C E(X)=0_;6!;+_;3@;+_;6!;= E(X )=0 _;6!;+ _;3@;+ _;6!;=;3$; V(X)=E(X )-{E(X)} =;3$;- =;3!; 3 r(x)=æ;3!; = 3 C 06 P(X=0)= 3 =; 0; C C _ C P(X=)= 3 =;ª0; C C _ C P(X=)= 3 =;ª0; C C P(X=3)= 3 =; 0; C E(X)=0_; 0;+_;ª0;+_;ª0;+3_; 0;=;#; E(6X+)=6E(X)+=6_;#;+= 07 P(X=-)+P(X=-)+P(X=0)+P(X=)+P(X=4) 430 r(x)=!%v(x)= 9 r(-9x+0)= -9 r(x) =9r(X) = X 3, 4, 5, 6 _ C P(X=3)= = =;3!; C 4_3 C P(X=4)= 3= =;6!; C 4_3 _ P(X=5)= 4= =;6!; C 4_3 C _ P(X=6)= = =;3!; C 4_3 E(X)=3_;3!;+4_;6!;+5_;6!;+6_;3!;=;(; E(X )=3 _;3!;+4 _;6!;+5 _;6!;+6 _;3!;=;:!6#:!; V(X)=E(X )-{E(X)} V(X)=;:!6#:!;-{;(;} V(X)=;!(; V(-6X+3)=(-6) V(X) V(-6X+3)=36_;!(; V(-6X+3)=57 09 X B(, p) E(X)=p=4 V(X)=E(X )-{E(X)} =8-4 = 47

208 V(X)=p(-p)= -p=;!; p=;!; =8 X 8 0,, 5 X B{64, ;8#;} E(X)=64_;8#;=4, P(X=)= C {;!;} {;!;} 8- = C {;!;} 8, =0,,,, 8 P(X 6)=-P(X>6) =-P(X=7)-P(X=8) =- C 7 {;!;} 8 - C {;!;} 8 =-8_;5!6;-;5!6; V(X)=64_;8#;_;8%;=5 E(X )=V(X)+{E(X)} =5+4 =59 =;@5$6&; a=56, b=47 a+b= , 3, 5, 7, 9, 3, 5, 7, X B{90, ;3@;} E(X)=90_;3@;=60, 0 Y Y=-X+5 P(Y=3)=P(X=) P(Y=3)= C {;!;} {;!;} 3 P(Y=3)=0_;3 ; P(Y=3)=; 6; V(X)=90_;3@;_;3!;=0 E(X )=V(X)+{E(X)} =0+60 =360, V(aX)=a V(X)=0a 0a =360 a =8 V(X)=5_;!;_;!;=;4%; V(Y)=V(-X+5) V(Y)=(-) V(X) V(Y)=V(X) V(Y)=;4%; Y=-X+5 E(X+Y)=E(X+5)=E(X)+5 E(X)+E(Y)=E(X)+E(-X+5) =E(X)-E(X)+5 =E(X)+5 E(X+Y)=E(X)+E(Y) ;!; X B{8, ;!;} E(X)=8_;!;=9 E(4X-3)=4E(X)-3=4_9-3=

209 f() :_! f()d=:_! (a +b)d E(X )=:) f()d=:) ;!; d=[;8!; ])= V(X)=E(X )-{E(X)} =-{;3$;} =;9@; V(9X)=9 V(X)=8 8 =:) (a +b)d =[;3A; +b]) =;3@;a+b= a+6b=3, f() ;3@; b=;3@; a=-;!; 04 V(X)=E(X )-{E(X)} =6-{E(X)} = {E(X)} =4 E(X)= ( E(X)>0) :_@ (3 +5)f()d =3:_@ f()d+5:_@ f()d =3E(X )+5E(X) =3_6+5_ =8 P{0 X ;!;}=:) ;!; {-;!; +;3@;} d P{0 X ;!;}=[-;6!; +;3@;]) ;!; P{0 X ;!;}=-;4 8;+;3!; P{0 X ;!;}=; 6; 0 :_@ f()d=:_0@ f()d+:) f()d =:) f()d+:) f()d =;4!;+:) f()d =;3!; :) f()d=; ; :_-# f()d=:!3 f()d =:)3 f()d-:) f()d =;!;-; ; =; ; 05 :_@0) f()d= :_@0) f()d=;!;_30_k=5k= k=; 5; ( ;30!0;+; 5; (-0 0) f()={ -;5!0;+; 5; (0 0) 9 E(X)=:_@0) f()d E(X)=:_0@) {;30!0;+; 5;}d+:) 0 {-;5!0;+; 5;}d E(X)=:_0@) {;30!0; +; 5;}d+:) 0 {-;5!0; +; 5;}d E(X)=[;90!0; +;3 0; ]0_@)+[-;45!0; +;3 0; ])0 E(X)={: 9º:-: 3º:}+{-: 9º:+: 3º:} E(X)=-: 3º: E(-3X+5)=-3E(X)+5=5 03 E(X)=:) f()d=:) ;!; d=[;6!; ])=;3$; 06 a=p(xæm)=0.5 b=p(-m X m) 49

210 _m 0 =m a>b c=p(0 X m) b>c a>b>c 07 P(r X-m r) X-m =P{ } r =P( Z ) =P(- Z -)+P( Z ) =P( Z ) ={P(0 Z )-P(0 Z )} =( ) =_0.359 = f() =m m f { }<f(m ) r =r f(m )=g(m ) r <r, m =m, f(m )=g(m ) =f(), =g() 90-m P{ 3 Z 0}=0.48 0, 90-m m-90 P{ 3 Z 0}=P{0 Z 3}= m-90 3= 0 m=30 0 X X N(7000, 600 ) P(Xæ800)=P{Zæ } 600 =P(Zæ) =0.5-P(0 Z ) = = C _0.0 _0.98 =0_0.0 _0.98 =0.004_0.98 X 00-X 3X-(00-X)æ60 4Xæ60 Xæ40 X B{00, ;!;} =00 m =m P(Xæm )<P(Yæm ) 09 X X N(m, 0 ) P(Xæ90)=0.98 m =m =»() =f() 90-m P(Xæ90)=P{Zæ 3} 0 90-m =P{ 3 Z 0}+0.5= E(X)=00_;!;=50, V(X)=00_;!;_;!;=5 X N(50, 5 ) P(Xæ40)=P{Zæ } 5 =P(Zæ-) =P(- Z 0)+0.5 =P(0 Z )+0.5 = =0.977 X X N(50, 0 ) P(Xæ90)=P{Zæ } 0 =P(Zæ) 50

211 =0.5-P(0 Z ) = = Y Y B(400, 0.0) E(Y)=400_0.0=8 V(Y)=400_0.0_0.98=7.84=.8 =400 Y N(8,.8 ), P(Yæ) P{Zæ } P{0 Z }æ , æ3 æ X X =0 E(X +3)=E(X )+3=_0+3=3 V(X )= 4= S = 0 N(m, 5 ) 6 X E(X )=m V(X )= 5 4=;@6%; 6, X = Y 4 6 Y=6X E(Y)=E(6X )=6E(X )=6m=80 m=5 V{ Y }= V(Y) = V(6X ) 4 3 m m 5 6 _;@6%; = 6 V(X ) 4 = =6 03 E(X )=0, V(X )= r 4 X N{0, r 4 } P{ X -0 X } =P 4 4r ª r º =P( Z ) =P(0 Z )æ P(0 Z )æ0.477, P(0 Z )=0.477 æ æ X B{44, ;!;} 5

212 =44 E(X)=44_;!;=7, V(X)=44_;!;_;!;=36 X N(7, 6 ) 5 X 6 E(X )=7, V(X )= 4={;5^;} 5 P(Z.65)= æ X N{7, {;5^;} } P(X æ73.) =P Zæ 4 ª ;5^; º =P(Zæ) =0.5-P(0 Z ) = = X X N(75.5, 3.5 ) 00 X E(X )=75.5 V(X )= 3.5 ={ 3.5 4} 00 0 X N{75.5, { 3.5 4} } 0 P(74.8 X 75.85) =P 4 Z 4 ª º 0 0 =P(- Z ) =P(- Z 0)+P(0 Z ) =P(0 Z )+P(0 Z ) = = X N(50, 5 ) 5 E(X )=50, V(X )= 3 X N{50, 0 P{X } =P Z 5 =P(Z -+4)æ0.95,P(0 Z.65)= } 07 s= P(0 Z.58)= m 99 % [ -.58_ 3, +.58_ 3 ] m 99 % 7.355, _ 3 = _ 3 = =6 = _ 3 = _ 3 =0.645 =.58 = = =6 _ =6_8= % m r r [Ǣ.96_ 3, Æ+.96_ 3 ] r r -.96_ 3 Ǣ m.96_ 3 Ǣ r m.96_ 3 r Ǣ m < r r.96_ 3 <, >3.9 > m 99 % a, b b-a=0.9 ;!; b-a=_.58_ =0.9 5

213 =.58 = = = 대단원마무리 Level P( Z k)= a =_k_ =4k k= P(0 Z )=0.475 P(- Z )=P( Z )=0.95 a=95 r 4r b-a= 34 = 35 5 r 6r d-c=_3_ 3 = 3 b-a d-c 4r 6r 3 3, ;5@; a+b= P(A;B) P(B A)= P(A) P(3 X 4) = 3 P(Xæ3) P(X=3)+P(X=4) = 4 P(X=3)+P(X=4)+P(X=5) a+b = =;4#; a+b 4a+4b=3a+6b a-b=0 a=;4!;, b=;8!; E(X)=_;4!;+_;4!;+3_;4!;+4_;8!;+5_;8!;=: 8 : E(8X+4)=8E(X)+4=8_: 8 :+4=5 0 a+;8!;+;4!;+b= a+b=;8%; P(X )=P(Xæ) a+;8!;=;4!;+b a-b=;8!; a=;8#;, b=;4!; E(X)=0_;8#;+_;8!;+_;4!;+3_;4!; =;8!;+;!;+;4#; =: 8 : E(X )=0 _;8#;+ _;8!;+ _;4!;+3 _;4!;=: 8 : V(X)=E(X )-{E(X)} =: 8 :-{: 8 :} =;6(4%; p+q=

214 03 X B{30, 3} 5 E(X) 30_ 3==0 5 =5 P(X=r)= ºC r {;3!;}r {;3@;} 30-r (r=0,,,, 30) ºC {;3!;} 3 {;3@;} 7 P(X=3) 3 = 34 P(X=7) ºC {;3!;} 7 {;3@;} 3 {;3@;} 4 = {;3!;} 4 - a 3 P(- a 3) =P{ 4 Z 4 } =P(-.5 Z ) =P(-.5 Z 0)+P(0 Z ) =P(0 Z.5)+P(0 Z ) = = = 4 04 f()=a +b a+0 :_! (a +b)d=:) (a +b)d =[;3A; +b]) =;3@;a+b= a+6b=3 E(X )=:_! (a +b)d =:_! (a +b )d =:) (a +b )d =[;5A;fi +;3B; ]) =: 5Å:+: 3ı:=;5!; 6a+0b=3 a=-;4#;, b=;4#; f()=-;4#; +;4#; f {;!;}=;ª6; 05 + = a-=0 4a- 34!%3 +4 4a a Y Y N(48, ) 7-48 P(Yæ7)=P{Zæ 4 } =P(Zæ) =0.5-P(0 Z ) = =0.0 X B(00, 0.0) V(X)=00_0.0_0.98=.96 V(0X)=00V(X)= X X N(500, r ) X E(X )=500 r V(X )= 4 r X N{500, 4 } 700 P(X æ700)=p{x æ 4 } 6900 P(X 6900)=P{X 4 } =500, = =4 08 =00 95 %, 4 r 4-=_.96_ r =_.96_

215 = % 4, k r k-4=_.96_ r k-4=_.96_ 3 0 r k-4=;!;.96_ 3 0 k-4=;!;_= k=5 대단원마무리 Level P(X=)=P(X=) C p (-p) = C p (-p) 6p(-p) =3p (-p) (-p)=p p=;3@; X B{3, ;3@;} V(X)=3_;3@;_;3!;=;3@; 0 X, Y E(X)=p +p +;#;, E(Y)=p +4p +;(; p +p +;!;= p +p =;!; E(X)=+p, E(Y)=3p +5 Y=X V(X)=E(Y)-{E(X)} V(X)=3p +5-(+p ) V(X)=-p -p + V(X)=;9%; ;9%;=-p -p + {p -;3!;}{p +;3$;}=0 p +;3$;+0 p =;3!; E(Y)=3_;3!;+5=6 03 X B{400, } V(X)=9 400 {- }=9 0 0 {9- }{- }=0 (9-0)(-0)=0 9-0=0-0=0 55

216 =0 X-5 04 Z= Z N(0, ) P(3 X 6)=P{ Z } =P{- Z ;!;} =P(- Z 0)+P{0 Z ;!;} =P(0 Z )+P{0 Z ;!;} =p +p ;!; 05 :)c f()d= ;A;+(b-a)+ c-b = b-a+c= A=[ f() ;!;] A=[ 0 ;A; b+ c-b c] c-b P(X<A)=;8A;+ =;6!; 8 a-b+c=;3$; - b-a=;3@; b-a=;3!; P(a X b)=b-a=;3!; 06 X N(60.5, 0 ) 0000 X 0 E(X )=60.5, r(x )= 3 =;5!; X N{60.5, {;5!;} } P(X 60)=P{Z 4 } 0. =P(Z -.5) =0.5-P(0 Z.5) = =

217