Calculo

 Cálculo Diferencial con “Mathemática”

!" & '&() &*+ $%, & *(-$! . #" #" & '& &+$. !& -$ !" #$% $! & $! % */$#" &! ( & . 0/& #" $! &+*$! ) $' " */-&! -&1& -& -&.2$. (+-& (*+$! (+#" *$+$. (! &31. '/ &) (!4 &.5+&$ -& / #/$-+$-( -&1& -& -& . . '" -& !/ . $ ( */$-(%&.&!1$#" +&#(++" 1(+ / ( -( ) 62" & / 1&+" . (-( -& *" 1( -&1& -& -& !/ 2&. -$-% &. 7) &+( -& 2& *$! -& / &) (#" 1+(-/#*( -&1& -&-& !/ 1+&#" 1&+( . -& " " 6 -& / $ / #" (8 $ #" 6 (+) /. $+!& & *9+) " (! -& / $ &:1+&!" $ $.*" 6 #$ $ / #" 6 -& 7) &+(! +&$. 2$ $ !&+ #" &! &+*$ +&'. 0/& $!" & $ #" $ ' &+*(! &#&!" (!% ( (;!*$ *&% / $-& " " 6 *$) #" ( !" 1+& 1(-+5 &)

7) &+(! +&$. #" &! &+*(! 7) &+(! +&$. &! & &#*" -& / #" 2$ 6 .$)$)(!

$ / $ #(++&!1( -& #" & *+& $

!/;#( 3 *(! -& 7)&+(! +&$.&!%-& (+)$ 0/& $ #$-$ 7)&+( +&$..& #(++&!1( -$ / ( / , !6.( / 7)&+( +&$. 4 &! &. #( 3 *( / #(++&!1( -& #" $ &! &. #( 3 *( -& 2$.(+&! $!(#" / $-(! $ .(! -& .$ #(++&!1( -& #" $ $+$ -&!" $+/ $ / #" !& /*" . 7)&+( +&$. 0/& !" );(."1(+4 1&+( .$ +&#/& #"$ 1&+)$ &#& % " 2$+"$ *&
2

2 Cos
1

Cosx Cos
2 1 2 3 2

2

2

2

Figura 1.22. Gráfica de funciones

a cos x

" )/.*"1."#$)(! &. 5 '/.( 1(+ / $ #( !*$ *& .$+&#/& #"$ =" & &. 1&+"(-(> !& )/.*"1."#$ 1(+ .$ #( !*$ *&%1&+( .$ .( '"*/- -& ( -$ &! .$ )"!)$
1.0

Sin x Sin 2x

0.5

2 0.5

2

Sin 3x

1.0

Figura 1.23. Gráfica de funciones

sen ax Cálculo Diferencial con “Mathemática”

&$

f :A⊂

→

, g:B⊂

→

-(! / #" &! +&$. -& ( &!

2$+" & +&$. & 1/&-& -& " " $! !" & *&! / #" &!4 $;. +. '/" ( -& " " 1(+= F'> :> = F'= 8 () =F'> ∩ -$ = B :> :> B -& " " 1(+= E'> :> = E'= 8 () = E'> ∩ -$ = B :> :> B -& " " 1(+= '> :> = '=:> () = '> ∩ -$ = B :> 8 B -& " " 1(+= I'> :> = I'= 8 () = I'> ∩ EL:∈ *0 '= ≠GM -$ = B :> :> B :> -& "" 1(+= > :> = ]8 () = >BL:∈ *0 = -$ '( = B'N :> '( :>∈ M $! #/$*+( 1+" &+$! (1&+$#" &! !( . -& () " $-$! (1&+$#" &! $. ) ( $! ( '&;+$" #$! , *" & & . ) " $! 1+(1" $! !) &-$-&! 0/& . !/) $ , &....