미통기-3-06~07(052~071)

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1 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 : k d=k+c k C : «d= + +C =0C + : k f()d=k: f()d k : { f() g()}d=: f()d : g()d =f() =f()[a, b] b-a b-a lim f( )D=:Ab f()d { D= =a+ k} :Ab f()d f() 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) 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 lim f{a+ } b-a =:) b-a f(a+)d=:ab f()d k= 5

2 F'()=f() : f()d=f()+c C : «d= + +C + =03C 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) lim 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=: (-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

3 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 b 3 c =f() f() :Ab f()d=:ac f()d+:cb f()d f() =f() :Ac f'() d f'(a)=f'(b)=f'(c)=0 a<b<c 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

4 3 :Ab f()d=a 07 lim :@/ (t +at-)dt=5 a lim :A/ f(t)dt=f(a) a -a lim :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() lim =6 - f()-g(0) 55

5 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 _ 4 :_@ f()d=3, :@4 f()d= f(+)=f(-) +4 :! f()d : f()d = = : f()d :! f()d=: f()d

6 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 ab f() g()=(-a)(-b)f() f() :_! g()d=0 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

7 6 pk p lim f{a+ } =:A a+p f()d k= 4 lim (+) +(+) +(+3) ++(+) =:)p f(a+)d =p:) f(a+p)d =f() =f() [0, ] f() g() k k- k lim [g{ }-g{ }] k= 5 f()=3-4- g()= lim f{ k} k= lim 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 = lim[- g{ }] k=0 =-:) g()d=:) f()d 58

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

9 7 f()= + [0, ] 0=º ««= f( )+f( ) lim [ ] 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=0 (, f( )) (, f( )) =««S()= A S() S(+)= k=0 a = 60

10 07 [a,b] =f() =a,=b S S=:Ab f() d a =f() b [c,d] =g() =c,=d S d =»() S=:Cd g() d c [a, b] =f() =g() =a, =b =f() =»() S S=:Ab f()-g() d a b Pt 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

11 0 ='ƒ+ ='ƒ+ = ;!; ;#; S=:Ab f() d S=:Cd g() d f() g() ;%;, ;3@;, {;3@;}, {;3@;} 3,, {;3@;} -, = = = 0 f()= + - =f( ) ;6%; ;6&; ;3$; ;#; ;3%; ;3@; {;3@;}3 {;3@;} ;5 7; ; 9; ;5 7; ;5 7; ; 9; S S={-;3@;} +[;3@;-{;3@;} ] {;3@;} +[{;3@;} -{;3@;} 3 ] {;3@;} =f() =f'() =f() 0 =f() _ ;!5$; ;!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

12 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 : = `_+ = :) {-( -+)} d=:) (- +)d =[-;3!; +;!; ]) =-;3!;+;!; =;6!; 06 f()= +a +a a f()

13 3 [ab] =f() =a=b S [ab] f()æ0 S=:Ab f()d [ab] f() 0 07 = - = - =k k k> ;5^; ;4%; ;3$; ;#; ;3%; = `_ =k S=-:Ab f()d f()= -5+4 S =f() f()= `_5+4 S S =f() S S 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 A =f() ==m B m 0<m< ;!; ;3!; ;4!; ;5!; ;6!; =m =_ A B = :)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!=;(; 64

14 09 =f() =f() a b 4 t=a t=b P v(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 tdt+:@3)5 (60-t)dt t :)3 5 v(t)dt=[ ])0 +[60t-t ]3@5) :)3 5 v(t)dt=(00-0)+( ) :)3 5 v(t)dt=75(m) 65

15 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 a b c d t :)c v(t)dt=:cd v(t)dt :)b v(t)dt=:bd v(t) dt PQ t 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

16 3 A() P t v(t) v(t) P ;3@; ;3$; ;3%; ;3&; ;3*; t 5 v(t) PQ t(0 t b) v (t) vœ(t) :)b {v (t)-vœ(t)} dt=0 0<a<b v (t) vœ(t) a b t t=bpq t=apq 0<t<b PQ 4 v(t) P t (0 t c) v(t) a b c t :)c v(t)dt=:ab v(t) dt P 3 P t=c 0<a<b<c 67

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

18 04 f()=- + lim 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%; S = =/ S S ;4#; ;8&; 06 P t v(t)=(t-)(t-a) P P a> ;3*; : 3º: : 3 : : 3 : : 3 : 69

19 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

20 04 f() = =0 =f() 3:) f()d v(t) PQ t(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 v Q (t) a b t t=b P :)a vœ(t) dt PQ P :)a vœ(t) dt t=bpq t=b P 06 AB P A B 3 P B A AB A P A A ;!; ;#; ;%; 7

(001~007)수능기적(적통)부속

(001~007)수능기적(적통)부속 0 6 06. C : k d=k+c k «+-, : «d= «± +C + =- : d=: ;[!; d=l +C : kf()d=k: f()d k : { f()+g()} d=: f()d+: g()d : { f()-g()} d=: f()d-: g()d : si d=-cos +C : cos d=si+c 008 : sec d=ta +C : cosec d=-cot +C