L4 LCC Limite

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Universidade Federal da Para´ıba - UFPB
Departamento de Cieˆncias Exatas - DCE
4a Lista de Exerc´ıcios - Ca´lculo I
Prof. Carlos Alberto Gomes de Almeida
1. Calcule:
(a) lim
x→2
x− 4
x+ 2
(b) lim
x→1
x3 − 2
2x2
(c) lim
x→0
x2 − 4
x− 2
(d) lim
x→−1
4x2 − x+ 1
x3 − 1
(e) lim
x→3
x3 − 3x− 18
x− 4
(f) lim
x→4
16− x
4+ x2
(g) lim
x→0
x2 + x
x
(h) lim
x→0
x3 − x
x
(i) lim
x→1
2x2 − 3x+ 1
x− 1
(j) lim
x→1
x2 − 3x+ 2
2(x− 1)
(k) lim
x→−1
x2 − 1
3x2 − 3x− 6
(l) lim
x→1/2
4x3 − 3x+ 1
4x3 − 4x2 + x
2. Determine os limites
(a) lim
x→5+
6
x− 5
(b) lim
x→5−
6
x− 5
(c) lim
x→1
2− x
(x− 1)2
(d) lim
x→0
x− 1
x2(x+ 2)
(e) lim
x→−2+
x− 1
x2(x+ 2)
(f) lim
x→5+
ln(x− 5)
3. Calcule os limites justificando cada passagem.
(a) lim
x→−2
(3x4 + 2x2 − x+ 1)
(b) lim
x→3
(x2 − 4)(x3 + 5x− 2)
(c) lim
x→−4
√
16− x2
4. Calcule os limites usando as propriedades de Limites.
(a) lim
x→0
(3− 7x− 5x2)
(b) lim
x→3
(3x2 − 7x+ 2)
(c) lim
x→−1
(−x5 + 6x4 + 2)
(d) lim
x→1/2
(2x+ 7)
(e) lim
x→2
x+ 4
3x− 1
(f) lim
t→2
t+ 3
t+ 2
(g) lim
t→2
t2 + 5t+ 6
t+ 2
(h) lim
s→1/2
s+ 4
2s
(i) lim
x→4
3
√
2x+ 3
(j) lim
x→√2
2x2 − x
3x
5. Calcule o limite, se existir
(a) lim
h→0
(4+ h)2 − 16
h
(b) lim
x→1
x3 − 1
x2 − 1
(c) lim
h→0
√
1+ h− 1
h
(d) lim
x→5+
x2 − 4x
x2 − 3x− 4
(e) lim
h→0
(2+ h)3 − 8
h
(f) lim
x→5+
√
x− x2
1−
√
x
(g) lim
t→0
(
1
t
√
1+ t
−
1
t
)
(h) lim
x→2
x4 − 16
x− 2
(i) lim
x→2
x2 + x− 6
x+ 2
BOM TRABALHO!!!
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