Lista2CalculoI2013
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Lista2CalculoI2013


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Universidade Veiga de Almeida
Curso: Ba´sico das engenharias
Disciplina: Ca´lculo Diferencial e Integral I
Professora: Adriana Nogueira
2a Lista de Exerc´\u131cios
Exerc´\u131cio 1: Calcule os limites dados abaixo:
(a) lim
x\u2192+\u221e
2x2 \u2212 5
3x4 + x+ 2
(b) lim
x\u2192+\u221e
2x3 \u2212 5
3x2 + x+ 2
(c) lim
x\u2192+\u221e
5x2 \u2212 3x+ 1
2x2 + 4x\u2212 7
(d) lim
x\u2192\u2212\u221e
4\u2212 7x
2 + 3x
(e) lim
x\u2192\u2212\u221e
2x2 \u2212 3
4x3 + 5x
(f) lim
x\u2192+\u221e
2\u2212 x2
x+ 3
(g) lim
x\u2192+\u221e
3
\u221a
x+ 1
x+ 1
(h) lim
x\u2192+\u221e
x2
10 + x
\u221a
x
(i) lim
x\u2192\u2212\u221e
6x2
3
\u221a
5x6 \u2212 1
Exerc´\u131cio 2: Calcule os limites dados abaixo:
(a) lim
x\u21927
\u221a
x\u2212\u221a7\u221a
x+ 7\u2212\u221a14 (b) limx\u21921
1
x2 \u2212 1
x\u2212 1 (c) limx\u2192p
1
x \u2212 1p
x\u2212 p
(d) lim
x\u21922+
\u221a
x2 \u2212 4 +\u221ax\u2212 2\u221a
x\u2212 2 (e) limx\u21923+
4x2
9\u2212 x2 (f) limx\u21923\u2212
4x2
9\u2212 x2
(g) lim
x\u21920+
\u221a
3 + x2
x
(h) lim
x\u21920\u2212
\u221a
3 + x2
x
(i) lim
x\u21923+
\u221a
x2 \u2212 9
x\u2212 3
(j) lim
x\u21924+
x
x\u2212 4 (k) limx\u21924\u2212
x
x\u2212 4 (l) limx\u21922+
x+ 2
x2 \u2212 4
(m) lim
x\u21922\u2212
x+ 2
x2 \u2212 4 (n) limx\u21925+
4x
(x\u2212 5)2 (o) limx\u21925\u2212
4x
(x\u2212 5)2
(p) lim
x\u21921+
x\u2212 3
x2 \u2212 1 (q) limx\u21921\u2212
4\u2212 x2
x3 \u2212 1 (r) limx\u21923\u2212
2x2 + 5x+ 1
x2 \u2212 x\u2212 6
(s) lim
x\u2192+\u221e
\u221a
3 + x2
x
(t) lim
x\u2192\u2212\u221e
\u221a
3 + x2
x
1
Exerc´\u131cio 3: Calcule os valores de a e b para que tenhamos a identidade
abaixo:
lim
x\u2192+\u221e[ax+ b\u2212
x3 + 1
x2 + 1
] = 0.
Exerc´\u131cio 4: Determine, caso existam, as ass´\u131ntotas horizontais e verticais
dos gra´ficos das func¸o\u2dces dadas abaixo:
(a) f(x) =
x2 \u2212 5
2x2 \u2212 4 (b) f(x) =
x3 + 5x2 + 1
x2 + 1
(c) f(x) =
x2 + 5x+ 4
x5 + 1
RESPOSTAS:
1) (a) 0 (b) +\u221e (c) 5/2 (d) -7/3 (e) 0 (f) \u2212\u221e
(g) 0 (h)+\u221e (i) 6
3
\u221a
5
2) (a)
\u221a
2 (b) \u22122 (c) \u22121
p2
(d) 3 (e)\u2212\u221e (f) +\u221e (g) +\u221e
(h) \u2212\u221e (i) +\u221e (j) +\u221e (k) \u2212\u221e (l) +\u221e (m) \u2212\u221e (n) +\u221e
(o) +\u221e (p) \u2212\u221e (q) \u2212\u221e (r) \u2212\u221e (s) 1 (t) \u22121
3) a = 1 e b = 0
4) a) y = 1/2 e´ ass´\u131ntota horizontal e x =
\u221a
2 e x = \u2212\u221a2 sa\u2dco ass´\u131ntotas
verticais.
b) Na\u2dco ha´ ass´\u131ntotas.
c) y = 0 e´ ass´\u131ntota horizontal e na\u2dco ha´ ass´\u131ntota vertical.
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