Listas e provas de Limites

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Tarefa 8 - Limites in…nitos
Calcule os seguintes limites
a) lim
t!�1
t2+3t�10
t+5
b) lim
x!�1
p
x2+8�3
x+1
c) lim
x!+1
p
x2+8�3
x+1
d) lim
�!+1
�4�1
�3�1
e) lim
x!+1
p
x2+8�3
x2�1 = limx!+1
(
p
x2+8�3)(
p
x2+8+3)
(x2�1)(
p
x2+8+3)
= lim
x!+1
(x2+8�9)
(x2�1)(
p
x2+8+3)
= lim
x!+1
(x2�1)
(x2�1)(
p
x2+8+3)
= lim
x!+1
1
(
p
x2+8+3)
= 0
f) lim
x!+1
1�12x3
4x2+12
g) lim
x!+1
3
p
x�x�1
x+1
h) lim
x!+1
2x
5
3�x 13
x
8
5+3x
= lim
x!+1
x
5
3 (2�x 13� 53 )
x
8
5 (1+3x1�
8
5 )
= lim
x!+1
x
5
3
� 8
5 (2�x� 43 )
(1+3x�
3
5 )
= lim
x!+1
x
1
15 (2�x� 43 )
(1+3x�
3
5 )
= lim
x!+1
x
1
15 (2�0)
(1+0) = +1
i) lim
x!�1
p
x2+8�3
x2+1
j) lim
x!�1
1�12x3
4x2+12
k) lim
x!�1
sen x
4x2+12 = 0 pois �1 � sen(x) � 1
l) lim
x!�1
sen x+x2
4x2+12 = limx!�1
sen x
4x2+12 + limx!�1
x2
4x2+12 = 0 +
1
4 =
1
4
m) lim
x!+1
sen 3x
2x
n) lim
x!+1
1�cos 3x
2x
o) lim
x!+1
�
sen 3x
2x
�2
p) lim
x!+1
1�cos 3x
2x2 sen x
q) lim
x!�1
1�cos2 �x
2x2
1