Calculo_Diferencial_LE03_Limites

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1
LE03 - Infinito e Limites
1. Calcule os limites para x→∞ x x→ −∞
(a) f(x) = − 1
x2
(b) f(x) = x2
(c) f(x) = −x3
(d) f(x) = x3 + x
(e) f(x) = x3 + x2
2. Avaliar os limies abaixo,utilizando os teoremas das
operac¸o˜es:
(a) lim
x→∞x
4 − x
(b) lim
x→∞
5x3 + x2 − 1
2x2 + x + 1
(c) lim
x→∞
(√
2x + 1−
√
2x
)
3. Calcule
(a) lim
x→∞(x
2 + x)
(b) lim
x→∞x
5 + x3
(c) lim
x→∞(−x
4 − x2)
(d) lim
x→∞
1
x
(e) lim
x→∞
−3
x2
(f) lim
x→∞
6
x3
4. Calcule
(a) lim
x→∞(x
3 − x2 + x− 1)
(b) lim
x→∞(−2x
4 + x2 − x)
(c) lim
x→∞(−4x
3 − x2 + x)
5. Calcule
(a) lim
x→∞
6x2 + x + 1
3x− 7
(b) lim
x→∞
4x3 − x2 + 2
5x3 + 3x + 1
(c) lim
x→∞
6x4 − x2 + 3
−3x2 + 5x− 1
(d) lim
x→∞
10x3 − 7x2 + 1
−2x4 + x− 1
(e) lim
x→∞
4x5 − x3 + x
3x5 + x2 + 1
(f) lim
x→∞
5x3 + x2 − 1
−3x + 7
6. Calcule
(a) lim
x→∞
√
3x + 1−
√
3x
(b) lim
x→∞
(√
x + 3−√x + 1)
7. Calcule os limites
(a) lim
x→∞
x√
x4 − x2
(b) lim
x→∞
2x + 1
x2
(c) lim
x→∞
(
1
x2
+
2
x3
)4
(d) lim
x→∞
5x3 − 1
x3
(e) lim
x→∞
2x2 + 3x + 1
x2
(f) lim
x→∞
x√
x2 + 1
(g) lim
x→∞
3x3 − 4x + 1
4x3 + 3x2 − 2
(h) lim
x→∞
x
√
x + 3
√
x + 1√
x3 − 1 + x
(i) lim
x→∞
x
√
x + 3
√
x + 1
√
x3 − 1− x√
x3 − 1 + x√x3 − 1− x
8. Calcule
(a) lim
x→2
2x2 − 5x + 2
5x2 − 7x− 6
(b) lim
x→9
x− 9√
x− 3
(c) lim
x→−3
(
x + 3
x− 1
)(
x− 4
x + 3
)
(d) lim
x→2
x2 − 4
x + 2
(e) lim
r→1
r2 − r
2x2 + 5r − 7
(f) lim
k→4
k2 − 16√
k − 2
(g) lim
x→−2
x2 − 4
x + 2
(h) lim
x→3
2x3 − 6x2 + x−3
x− 3
(i) lim
z→−2
z − 4
z2 − 2z − 8
(j) lim
z→5
z − 5
z2 − 10z + 25
(k) lim
h→0
(x + h)2 − x2
h
(l) lim
h→0
(x + h)3 − x3
h
(m) lim
x→0
(x + h)4 − x4
h