Regulación de Cálculo: Conceptos de Funciones Continuas y Derivadas, Apuntes de Cálculo

¡Descarga Regulación de Cálculo: Conceptos de Funciones Continuas y Derivadas y más Apuntes en PDF de Cálculo solo en Docsity!

Regularización Calculo

! (^)! " #$%^ "^ #$% & '())^ *&+, (^) -. / 0 '()) (^) *&+, (^) -. / ! #$%

2($3$$450$''66))0785)''66229:;2''6''$#<=#1''<1= <%51 "^ 1$#<%

? ' ,/ #$% ' "^ '^6 " ' @#;< ?

!( 'AA^ B^ ,'^ ,/

#$% '^ ,'^ "^ '^ ,C',

" ;

D)4D;#

EBF6!

5<1 G! /^ " BHEG! / '^ #1#0# #1#0# I.6FG!/!^ '^6 ' :$J ;#1# ? 3

#$% ; '^ '^ #$1;^2 '^ #$1;

?? ' K#

" L <^ 'M, (^) @E6 ,N, $1 3 #^ $1#05 / 6F6!6 (^) ,' B "^! K0^ L^ ', #$% (^) ; "^ #$%^ ; 0#1#1#</^ " (^) @6FG! / (^) ,',, N O^ ,

$1#055 (^) $1 # ? / " ,$1 (^) ; ,',^ "^ #$%^ # 0 'M,^ M'*,

Derivada: Es un limite especial, que nos dice como cambia una función de manera infinitesimal.

f’(x) es la derivada de la función f(x)

Ejercicio: Calcula la derivada de f(x) = x

Significado de la derivada

8S!/ '^ #$%^

:#1#5T# ' 8G! /

T (^) 'MA (^) T 2 :##0#^ U^ L V U WK!^ U W<L C Q :' V X/ ' C! #$% Y^ !5T

/ V^ ' 0C

8S! / "

' C!

T 'MA^ T

W;4$7< :505 "^!

Z

@6!6 '^ *,C^ U W;4$7< 8B!6 '^!^

? U^ 86G!6^ "^ +[^ U @X6^ "P^ U^ 86G!]!^ ?

8^6 " !

?

Q :5_

?? L L< ' L U ' S<?^ '^ '''''^ ' L5)L

' :#05T#

P;1`$;15; %; (^) 0< ', (^) U S 5; +"+'+ J^ 2--35)L''4'D05T#'

S

a (^5) b )L; 8D05T^ /^ '^ 8B!

W! " ,C',

U V W! c !6 (^) X< A, (^) "^ 8#05T^ / ' :#0# @' (^) )L <' (^) A&', H0 W! %; 8#05T (^) / ' :#0# %; dU^ " :5_2;:eee):#05T#':#0# <L W! #$% 8G!-X (^) / ' :#0# W! 'MA W! U^ 86B!^ " f _% f#05T#'R',f0'R,'T24)T ' ,+&'f 8S!6 '

V

5#05g "^ D05h#5^ Q^ 5h#05($5h S i dM , C+,'C,+C " ,C,&,'C

J

86X "^ G!G- C/

< :5#0 /^ " C,&CNC,,C&, 3 G^j / ' k:: 5 7d&

S

V " *&C 5 +&'+

C

U L

V l h (^) */ 0 V m ($$^ n ,' E-EK ( 2 o ? U ($^2 ' o.

" ' Ko ? " (:2$( " (5h( " E.EK

Y G#05T#5^ ,/^

V (^5) ,CF 5#:

Y G#05T#5^ ,/^

V (^5) ,CF ,,]

Ejercicios:

V (;%<1< 3

" D)D$1<

BHEG!6 O^ B`(^ U

" EBBG! /

5'<1D0#'(:<1w'D)5w5s:'s`s:D(D2%1m;/]'''BEB#+0/BA5#+I/Y,C&+"',C,9Y,+&/ D)5 (^) Y +0+ ,d ' (^2) <50#D(DD<0;(5 2 K0$s; " 3 6(%<$# ? / 'C (^) D)(< (^) <^ ,^ BH[P^ /

" ' 6(;1 ,+&^ / BHE Y +&mY,C&C/"',C&C E. "^ ',C,^ (;1`;4)/ (D1#(;0;#

"^ '^ ,C+^

V D(D# +^ #D)5 Y+&*/ ' ' d ()1#7#^ <'^ D)(D7^ /^ (^3) / W! x^ H y K$(;

2 ????^?

($$$zy ? ??? { y k1$45; "

'??^ V D)(5?^?

V

"^ '^ ,C&,^ D(D#<0|D)hDL c^ /^ y^ Y8/^ " jo '? o#

(;15<4</^

V 7C Y } (^) ' '^ '

Seno = Sen(x)

Coseno = Cos(x)

Tangente = Tan(x)

Cosecante = Csc(x)

Secante = Sec(x)

Cotangente = Cot(x)

Tarea:

L< (;1# f,C^ / Q `<5; 6)0()1#^ !C (^) /

:' 5<1^ Bt!^

" U L1U

" R E;D Y^ R&,C

S

" (^) 5<1 Y`/ "

D)(</

Q (^) 6-U^ "^ '^ )~0(;1D0<^ n^ < 3 #k7#^ ' k:: U 54<; Q (^) " 3 ^ +^ D)(D0h^ ' @/ "^ +G'^ (;15$4^ '^ ,/^ G<0// 5)(;1D^ i (^) ,/ " ' ))0(;1D0< ' F W! U L d '^ ' o# 5<15< ' </ " d ^ 5<15< ' @S

' D)(<(

C, (;1<`)4<^ /

" h5<1##) ' 'A] #(;D (^) G@ 'A,*,Cd ' ,/ Q f,"'C^ (;1#(155(;1#T#h#5^ +^ BHEBGXBHEG^- Q (^) <' (^) K<4# z (^) X;$# 2 2 4D)(#^ KX Q L " (^) 6(5<1D0<##

Q L$2(Äm55<1#0<[(;D+0+#<0#''C0(;DB!+ */ 5<1^ <#

Ejercicio 3.-

+,18 j1(15#

"^ +,A+M^

' ,A+M+[ ' (^) 6- K7<#k<1`) (^) 5;1;%)(

|k;

T 'MA [^ C (^) AC H ,', " <' " 6Ix Bk<1) (^) T<L k1^ #$%$5;;^ #<^ :)4%<^ 'r^ )`;%)( k(<4^ G^ V X)$5<# 2 +,18 ^1< (^) N , Y+,18 ^1< (^) N ,/ ? #$% " #$%

15. 1 V (^1) 'MA (^) Y 1< / V Y (^) +18 (^) j1<5$# V 2 ##1<0$$ ? '

Y 1<

? (^) V / V " (^) :5_2+5$9B+1(#'hD1<5$ÄD< U @ V % 1; 1 O '^ '^ ' '+,[XP ? (L#1<5$ (^) É 5$^ ,++ ' G1<55$ ,+C Y 1<^ / V " CT G$%) ? (^)? 662 b 5$# V 2$% (^2) .5;% ' .5;% CT

1. (^) G1<55 ,+C^ '^1 É 5$^ ,++ #$% ,[5^ ,,*,+^ Y^ 1<5^ ,/^ V,C ? (^) % FÑGF^

C,',,+C ' 1

É+,',,++ " (^1) 'MA CT FH

#1 ++,++ Y 1<5^ ,/?^ C

L

C

V $1:) 5#1#1<55#

?Z '

++M,,++ /^ $$% FÖGF@X ,+C^ ' G1k54 ,++ 'C@ 61 ++,++ (^) Y T55 (^) ,/?^ C FH (^) C (^) #_##5 ,+,1@ ,/ +C " Ü ' Y A+,',,++^ '^ # " (^) C C,A+,',,9,A+,, 2

 5<1T#0##>$^ '^ 5<1TD0<^2 Y>5>^ ? ##>5> ? / ' #; ? '

? ##; ?

0 / YD05;^ ' 0_ â G;$5; ' (^)?

V ' #;?^ ' ;' ? #< GD05; ' 0_ G;$5; ' (^)?

V #; ? (^) ' ;' ? #< " G;05; ' 0 / V ' G;05; ' 0 / V "m ' 5<1T#0#< (^) Q  5<1T#0#(52$5 '^ 5<1T#0#<

WEK[G!6 "^ #$%^ (;1505T/^ '^ (;1#0#^ "^ #$%^ (;1#0#D)(DT#^ '^ (;1#0#5D)(#1#(;1#T#

`0 T^ 'MA (^) T T '() T " #$% (^) (;1D0#;#D)(#T# ' ,/ 5D)(#0#(;1#T# T 'MA^ T

" #$%^ E;1#0#5D)(#T#^ ',]^ N #$%^ D)(#0#(;1#T#

T$() T^ T ' () T ä H^ ,,

" E;1#0##$% ^ D)(#T#^ ',]^

(;1#T#T$() ' -BHEG! /^ T ' () (^) T

#$% ^ D)(#T#^ ',]^ " D)(</ Q

`(;1#5# '

D)(#0/

T (^) '*A ' " H ` #$% D)(#4#5T /^ '^ BHEG! / #$% (;1#T#^ F)^ T

T ' $)T

#$% BHEB!6BHEGX6 ' (;1#4##(;1#T/ '^ BHEG!/

T 'MA T

#$% D)(#055D)4#T# ' ,* ' E;1#0#(;1#T/

"

#$% D)(#055D)4#T# ',*

'

#$% (;1D0#(;1#T#

Ä() T T 'MA T T 'MA T

D)(#0##$1%) 5)^ ' (;1D0$T1)(;11$Tq1 2 n^ U ,' (;DD0# ' K0 D)e< U "

e(w<5(;1D0##'9:<'(;1D0#'|D2(D3''5<1#!#(;DD0,L$"

Eo " d Q L V (^) ' (^80) :# " (^) 64%; #105< (^) ' 5h#1#0 /

L

V ' K 6 $1D0(/ V '^6 Q

L

V (^) " R&'f (^) W! C!

L

V "^ ', *&C'f&NC C!

L

V (^) " (^) EKBG!/

L

#; C0 6FB! / 5!

L

U (^) "^ '

D)(5 C&,

,' E;1^ Y^ C, / L

V " #1#0 V / 5 C

L# " !BHEBj6 5(;%D0^ / L U (^) "^ ,'^ 6FB!^ !EKFB! !C

S

? 2 C' 61 Y^ 0<^ /

!C <

S

V (^) " 'C#= ' @!

S

V (^) ' (^) BHKB! /

L

V " ' E5<1 GE! /