Calculo_I_2012_T02_Lista_07

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Ca´lculo I - Lista de Exerc´ıcios no¯ 7 - 1o¯ semestre/2012
1. Esboce os gra´ficos, determine o domı´nio e a imagem de cada uma das func¸o˜es dadas abaixo.
(a) f(x) = 3x (b) f(x) = (0, 4)x (c) f(x) = e−x (d) f(x) = 1+ ex
(e) f(x) = ex−3 (f) f(x) = ex+2 (g) f(x) = e|x| (h) f(x) = e−|x|
(i) f(x) = e−xsen x (j) f(x) = e−x
2
(k) f(x) = log3 x (l) f(x) = log 1
3
x
(m) f(x) = ln(x− 1) (n) f(x) = ln(x+ 1) (o) f(x) = ln(−x) (p) f(x) = ln(1− x)
(q) f(x) = ln |x| (r) f(x) = | ln x| (s) f(x) = | ln |x| |
2. Em cada caso, especifique o domı´no da func¸a˜o dada.
(a) f(x) = ln(3x− 4) (b) f(x) = x ln x− x (c) f(x) = ln x2
(d) f(x) = ln(x2 − 1) (e) f(x) = ln(4− x2) (f) f(x) = ln(x3 + 1)
(g) f(x) = ln
√
5− x2 (h) f(x) = ln
√
x2 − 3 (i) f(x) =
√
ln |x+ 3|
(j) f(x) = ln ln x (k) f(x) = ln ln |x| (l) f(x) =
1
ln x
(m) f(x) = ln
x+ 2
x− 2
(n) f(x) = ln
x− 2
3− x
(o) f(x) = ln
√
x− 2
3− x
(p) f(x) =
√
x2 + ex (q) f(x) =
x+ 1
ex − 5
(r) f(x) =
1√
3− ex
3. Calcule os limites:
(a) lim
x→+∞ 3x (b) limx→−∞ 7x (c) limx→−∞ ex
(d) lim
x→+∞(0, 16)x (e) limx→+∞(2x − 3x) (f) limx→+∞
1− 2x
1− 3x
(g) lim
x→+∞ 2−x (h) limx→−∞ 2−x (i) limx→+∞(2x + 2−x)
(j) lim
x→+∞ log3 x (k) limx→0+ log 13 x (l) limx→0+ ln x
(m) lim
x→+∞ ln
x
x+ 1
(n) lim
x→+∞[ln(2x+ 1) − ln(x+ 3)] (o) limx→1 ln
x2 − 1
x− 1
(p) lim
x→+∞
(
1+
2
x
)x
(q) lim
x→+∞
(
1+
1
x
)x+2
(r) lim
x→+∞
(
1+
1
2x
)x
(s) lim
x→+∞
(
1+
2
x
)x+1
(t) lim
x→+∞
(
x+ 2
x+ 1
)x
(u) lim
x→0(1+ 2x)x
(v) lim
x→0(1+ 2x)
1
x (w) lim
x→+∞
(
1+
1
x
)2x
(x) lim
x→0
e2x − 1
x
(y) lim
x→0
ex
2
− 1
x
(z) lim
x→0
5x − 1
x
UFMS / CCET Disciplina: Ca´lculo I - Turmas: 1 e 2 Professor: Celso Cardoso