Ayudanta 4 - Rodrigo CofrÇ

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ĺım
n!"
!
n + (!1)n
n
" #
n
"
n + (!1)n
n
$
ĺım
x!0
sin
%
ln(máx{x2, x2 cos(1/x)})&
1
x2
'
(
· x2
ĺım
x!2
(x2 ! 1) = 3
ĺım
x!3
f(x) = 6
f(x) =
)
*+
*,
2x x < 3
8 x = 3
3x! 3 x > 3
ĺım
x!1
x3 ! 6x2 + 3x + 2
x3 + x2 ! 3x + 1 !3
ĺım
x!4
x! 4
x!
"
x! 2
3
4
ĺım
x!0
-
x2 + p! p-
x2 + q2 ! q
q
p
ĺım
x!a
xm ! am
xp ! ap m, p # Z
+ m
p a
m#p
ĺım
x!a
x3 ! a3"
x!
"
a
a # R+ 6a2
"
a
ĺım
x!a
n
"
x! n
"
a
m
"
x! m
"
a
n, m # Z+ mn a
m!n
mn
ĺım
x!!
sin(x! !)
x2 ! !2
1
2!
ĺım
x!"
sin(x)
" ! x
ĺım
x!1
tan(x! 1)
x3 + x! 2
1
4
ĺım
x!0
1! cos(2x)
sin(3x)
c k
f(x) =
)
*+
*,
|x2#1|
x#1 cos(
"
2x) x < 1
a x = 1
x#b$
x+3#2 ! 4 x > 1
R a = 0 b = 1
[0, 1] 0 $ f(x) $ 1 x # [0, 1]
c [0, 1] f(c) = c