(001~007)수능기적(적통)부속

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2 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

3 : sec d=ta +C : cosec d=-cot +C : e d=e +C a : a d= 5+C a>0a+ l a : l d= l -+C : f()d=f()+c : f(a+b)d=;a!;f(a+b)+c a+0 f '() : d=l f() +C f() : " a - d =a si h{-; ; h ; ;} : " a + d: d a + =a ta h{-; ;<h<; ;}. :Ab f()d=[f()]ba=f(b)-f(a). :Ab kf()d=k:ab f()d k. : f()g'()d=f()g()-: f '()g()d :Ab { f() g()} d=:ab f()d :Ab g()d :Ab f()d=:ac f()d+:cb f()d :Ab f()d=-:ba f()d :Aa f()d=0. S=:Ab f() d =f() 4. a d :A/ f(t)dt=f() d d :?/ a f(t)dt=f(+a)-f() d a b O 5. abk f(). V=:Ab d=:ab { f()} d =f() lim ;K+! f{;k;};!;=:) f()d O a b lim ;K+! f{a+;b;k};b;=:aa b f()d=:)b f(a+)d. C =f() =g(t) : f()d=: f(g(t))g'(t)dt. P t v(t) t=a t=b P :Ab v(t)dt :Ab v(t) dt 009

4 0~ f()=6 +a :) f()d=f() a :) (-)d :) (-)d= :) (- )d f()=6 +a :) f()d=:) (6 +a)d=[ +a ])=+a =[;!; -;!; ])=;!;-;!;=;6!; f()=6+a +a=6+a a= :_! (-) d 0 00 = P() h() :) ta h()d ' ' = P() '= ` h() ta h() ta h()= :) ta h()d= :) d=[ ])= O P(, ) h() :_! (-) d= :_! (-+ )d= :_! (- + )d 4 =[ - + ]_!= AB =BC =B=90 A B C ABC AB B C C B B B B B«BC AB C C C C«- lim B C k= B«B«B... C«C«C 0 00 :) (+)( -+)d :) (+)( -+)d= :) ( +)d =[ +])= += B C BC =k B C =kbc k k B C = BC = ( BC =) k B C ={ } lim - - k B C = lim { } k= k= = :) d=[ ])= B A B C B C B C B C C 00

5 :) - d 5 0 < -<0 -æ0 :) - d= :) (-)d+ :! (-)d 5 =[- ])+[ -]!= += 0 05 k f()= lim f {+ } k= l l l l 5 l 6 lim k= k f {+ } = :! f()d = :! d =[l ]!=l =f() g() g()= :?/ f(t)dt g() g() g() 5 7 g{ } g{ } g(4) =f() O 4 f()=a(-)(-4)(a>0), g()= :?/ f(t)dt g'()=f(+)-f()=a{ --( -5+4)}=a(-), g'()=0 = a>0 =g() = g() g() 05 :) ' d 4 5 :) ' d=[ ;#; ])= 04 a :_aa ( +)d=;4!; 50a :_aa ( +)d= :)a d=[ ]a)=a a = a = ={ } a= a=50_ =5 5 09~ :) (+a)d=4 a 0 f()=+ :_! { f()} d=k{ :_! f()d} k 4 5 :) (+a)d=[ +a])=+a=4 a= ;6!; ;!; ;!; ;@; ;6%; :_! { f()} d= :_! ( ++)d= :) ( +)d=[;!; +])=;*; :_! f()d= :) d=[])= ;*;=4k k=;@; 0

6 4 009 [0] f() f(0)=0 f()= (0) f'()>0f"()>0 :) { f ()-f()} d k k lim [ -f{ }] k= k k lim [ -f{ }] k= k k lim [ -f{ }] k= k k lim [ -f{ }] k= k k lim [ -f{ }] k= :) { f ()-f()} d= :) { -f()} d k k = lim [ -f{ }] k= k k = lim [ -f{ }] k= O =f - () =f() = k f()= + lim f{+ } k= k k lim f{+ }= lim f{+ } ;@; ;!; k= k= =;!;:! ( +)d= f()= a b =g() g(0)=0 :A a g()d-:) a f()d= a g()=(-a) +b g(0)=0 -a +b=0 b=a g()=(-a) +a a a a a : g()d- : f()d= : {(-a) +a } d- : d a 0 a 0 (-a) a a =[ +a ] -[ ] 4 a 4 0 =6a -4a =a = a = =f() + f '() ( <) f '()=[ - ( >) =f() =- f()=f(-) f(0)=0 f()> f() :!/ f(t)dt= -a +a f() a ( ;!; +C (- <) f()= { -+C (<-) C C C 9 -+C (æ) f()=f(-) :!/ f(t)dt= -a +a = 0=-a+a a= :!/ f(t)dt= - + f()= -4+ f()=6 6 0

7 9 004 =f() = ' ' '5 '6 f '()=a(-)(+)(a+0) f()=: f '()=: a( -)d=a{ -}+C C, f() f(0)=0 C=0, f()=a{ =' -} f()=0 =0 = ' 00 f()=a+b g()=e f(g())= :)/ f(t)g(t)dt-e + f() f(g())=f(e )=ae +b ae +b= :)/ f(t)g(t)dt-e + ae =f()g()-(e +e ) f()g()=ae +e +e =e (+a+) a=b=a+= f()= =f() =f() f()= f()=- f(0)=- :) f '() d O - <> f '()>0<< f '()<0 :) f '() d= :) f '()d- :! f '()d=[f()])-[f()]! ={ f()-f(0)}-{ f()-f()}=f()-f(0)-f() = -(-)-(-)=8 00 f() f( f())= :)/ f(t)dt- ++ ` 0 - f()=a+b a(a+b)+b= :)/ (at+b)dt- ++ a =a+b-+=(a-)+b+ a-=0b+=a a=b= f()=+ += 00 f() f()-:)/ e f(t)dt= f ''(0) e f ''() f() f()- :)/ e f(t)dt= f '()-e f()=0 f '()=e f() ` f ''()=e f()+e f '()=e f()+e e f() =e f()+4e f(), f(0)= f ''(0)=f(0)+4f(0)=6f(0)= f() :_! f()d=f{-æ }a+f(0)b+f{æ }a 5 5 ab ab :_! d=a+b+a a+b= :) d=[])= :_! d=;5#;a+;5#;a ;5^;a= :) d=[;!; ])=;@; a=;9%; b=-: 9º:+=;9*; 0

8 5 00 :) ( +)d = + = f() f(-)=-f() f(0)+f()= f '(0)=f '() O O :) f()d=;!; f {;!;}=;!; f(0)=0 f(0)=0 [0] AB A-B A-B= [{ } +]- = - = 5 0 A-B = = æ = f() :@/ f(0) :@ f(t)dt=4+a+a+6=0 :@/ f(t)dt= -+ f(t)dt= +a+ a=- f()=- f(0)=0-= ;[!; d 0<a<b :Ab! ;[!; d :@Ab ;[!; d : ;[!; d 'b : ;[!; d : ;[!; d 'a :Ab ;a!; ;b!; a b b :Ab d=[l ]ba=l b-l a=l a b b b : d=[l ]@ba=l b-l a=l =l a a a 4 9~ f() f(+)=f(),. f()= { ( <) 9 -+ ( <) :_aa f()d=, a O ( (0 <) :_aa f()d= :)a f()d= :)a f()d=, :) f()d= _(+)_=, f(+)=f() :) f()d= :#6 f()d= :^9 f()d= :)9 f()d=6 :)9 f()d+ :(a f()d= :(a f()d=, :( 0 f()d= :) f()d= a=0 04

9 0 04 f()= -a k lim f{ }=f() k= a 4 k k lim f{ }= lim f{ } k= k= = :) f()d= :) ( -a)d=9- a 9- a=-a a=6 a= 0 f() :) f()d 4 f(0)= f '(0)= 0<a<b< f '(a) f '(b) (0) f "()=e ;!;e- ;#;e- ;%;e- ;&;e- ;(;e- f'()=e (0<<), f()=e (0<<) e=f '() f '() :!/ ed :!/ f '()d, e f() :! e d :! f()d :) f()d=:) f()d+:! f()dæ:) e d+;#;e=;%;e- 0 f()=(-) +5 F() F()= :)/ f(t)dt g() F(g())=;!;F() g'()=0 4 F'()=f() f(g())g'()=;!;f() = 4 f(g()) f()=(-) +5 = :) f(t)dt= :) f(t)dt = = 0=0_ =4 4 f() f()= -- t(tæ-) - t f() g(t) q :_! g(t)dt= +q f'()= -=(+)(-) f'()=0 = =- (- t 0) g(t)=[ f(t) (0 t ) :_! g(t)dt=:_0! dt+:) f(t) d= (q ) 4 4 O +q=4+=7 7 - =»f()» 05

10 4 00 f()= +a+b (aæ0b>0) [0] 0=º ««= [ ] f( ) A (k=) =f() A =f() [0 ] =f() f() g() k k- k lim [g{ }-g{ }] k= 4 :) g()d :) g()d :) f()d :) f()d :) {f()-g()}d O A k A º k k- - 0 k k- k - k [g{ }-g{ }] =- g{ } k= k=0 f() g() =- :) g()d= :) f()d A +A«= 7 + 8k lim;k+! A A +A«=;!;[f {;!;}+f()]=;!;{ +;A;+b++a+b}= a=0b= f()= + 8k k k lim ;K+! A =8 lim ;K+! f { }=8:) f()d= =f() P(af(a))Q(bf(b)) F() F'()=f() 4 P Q =f() O a b f() f()=:a/ {+si(t )} dt f''(a)='a(f )'(0) {a 0<a<æ } 4 ; 0; ;5!; ; 0; ;5@; ;!; f()=:a/ {+si(t )} dt f'()=+si( ) f"()= cos( ) f"(a)=a cos(a )='a ' cos(a )= a = { 0<a <; ;} 6 (f )'(0)= = = =;5@; f'(a) +si(a ) +si ;6 ; F() [ab] F(b)-F(a) b-a :Ab { f()-f(b)}d PQ (b-a){ f(a)-f(b)} PQ f(b)-f(a) F'(b)-F'(a) F(b)-F(a) = + b-a b-a b-a 06

11 :)4 (-)d :)4 (-)d= :)4 ( -)d=[ - ]4)=64-6= O, OAB. AB ( ) Pº(=A), P, P,, P «, P «(=B) P «(=B) P «P«P«P«P«P«O P Pº(=A) 9~ :) d S ( k ) OP«P«, lim ;K+!S :) d=[ ])=-0= =, P, P, P, P, P P. OPA OPB X, E(X) ; ; ; 0; ;9 ; ;8 ; ;7 ; :) e d e - e + e + e - e + :) e d=[e ])=e - PμOPμ = _ = (m=0,,,, -) 4 k P«OP«=k_ = (=,,,, ) 4 4 k k S = _ _si = si k lim ;K+! S = lim ;K+! si =:) si d =[- cos ])= 07

12 :) (4 +a)d=8a :) (4 +a)d=[ +a])=+a=8 a= f() :)/ f(t)dt=e +a+a f(l )(a ) e e :)/ f(t)dt=e +a+a f()=e +a =0 0=e +a=+a a=- f()=e - f(l )=e l -=-= =f() f() :Ab f()d=, :Ac f()d=0 f() F() =f() f() [0] 0=º ««= O a b c F(b)=F(a)+ (c, F(c)) =F() -<F(a)<0 F()=0 F"()=f'()=c f'()>0 (c, F(c)) =F() () =m m m- k=0 f( ) m - k=0 f( ) f( )+f( ) lim ;K+! [ ]=:) f()d - f( ) :) f()d f( ) k=0 k= f() [ ] - k=0 f( ) - k=0 [ ] f( ) m- k=0 f( ) m [ ] =f() O m- =f() O - 08

13 :) (-) d ;#; ;%; f() f()=;; 7 ;; -:! f(t)dt+[ :! f(t)dt] ;&; 0:! f()d :) (-) d =:) (- + )d+:! ( - )d=;#; f()=;; 7 ;; -:! f(t)dt+[:! f(t)dt] :! f(t)dt=a (a ) f()=;; 7 ;; -a+a a= :! f()d=:! {;; 7 ;; -a+a }d=4-a+a a -4a+4=0 (a-) =0 a= 0:! f()d=0a= a f()=-(+a)(-a) b :_ab f()d=a, :Ba a b f(-b)d=b :_ab f() d f() f(-)=f() f()=f(+4) -A+B -A+B -A+B A+B A+B :_ab f()d=a:)a f()d=b :_0B f()d=:_ab f()d-:)a f()d=a-b :_ab f() d=:_0b {-f()} d+:)a f()d =-(A-B)+B=-A+B :) f()d=6 :) f()d=6 :_0@ f()d=6, 4 :) f()d= :_-$ f()d :_-$ f()d=6 :_0$ f()d= :_-$ f()d+ :_0@ f()d= :_8$ f()d :_8$ f()d=

14 4 50~ =f(), f(0)=f()=0. k 7 lim f{ }=, f '(0) 4 k= O =f() m f(m) 0 A. 5 A X, E(X) ;&; f() :#6 f '() =f() (4, 8), (4+, 8+), (4+, 8+5), (4+, 8+7) k [k, k+] =f() f()d=a, 6a 4 =f() (, 7), (4, 8), (5, 0), (6, ). f()=+4 ( 4), f()=-5 (5 6) [4, 5] f()= +q+r f '()=+q f() f '(4)=8+q= `f '(5)=0+q=, =, q=-7f(4)=8 r=0. f()= -7+0 (4 5) a=:#6 f()d=:#4 (+4)d+:$5 ( -7+0)d+:%6 (-5)d 7 =[ +4]4#+[ - +0]5$+[ -5]6%= 67 6a=6_ = ;(; 5 f()=a(-)=a( -) (a<0) k lim ;K+! f{ }= :) f()d= :) a( -)d 7 7 =a[ - ])=- a= 6 6 a=- f()=- + f '()=-+ f '(0)= f() :)/ f(t)dt= +4, f(0) f() :)/ f(t)dt= - -:) f(t)dt f(0)=a 60a 4 :) f(t)dt=k k :)/ f(t)dt= - -k = :) f(t)dt=--k=kk=- k=- f()= -4+ f(0)= 60a=60_ =40 40 :)/ f(t)dt= +4 f()= +4 f(0)= 0 +4=

15 f()=e [] =º ««= (00)( 0)( f( )) A (k=) lim A 4 k= e -e (e -e) e e -e e - e =e =f() lim;!; f{m+;k;}<0 m k= - O 6 =f() A lim ;!; f{m+;k;}=:) f(m+)d= : f()d m=---45 m+ : m k= f()d<0 m 7 m m+ O º k k =+ f( )=e +;K; k A = _{+ }_e +;K; k lim A = lim {+ }e +;K; k= k= = :! e d= [[e ]!-:! e d]= e [0; ;] f() f {;4 ;} f() g() g()= : { +f()}d, f()g()=- +8 g() f()=a +b+c (a+0) g()= ;!; (+a) +;B; +c+c (C ), f()g()=(a +b+c)g()=- +8 g() +a=0 a=- (- +b+c){;b; +c+c}=- +8 b=4, c=0, C=0 g()= :) ; ; f(t)dt= cos :)/ f(t)dt=si :? ; ; f(t)dt {0 ; ;} ;5!; ;4!; ;!; ;!; cos :)/ f(t)dt=-si : / f(t)dt ; ; -si :)/ f(t)dt+cos f()=-cos : / f(t)dt-si f() ; ; =;4 ; ' - :) ;4 ; ' ' ;4 ; ' f(t)dt+ f {;4 ;}=- : f(t)dt- f {;4 ;} ; ; f {;4 ;}=;!; 0

미통기-3-06~07(052~071)

미통기-3-06~07(052~071) 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()