Limites - Parte 2

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Ca´lculo I - Lista de Exerc´ıcios no¯ 6 - 1o¯ semestre/2015
1. Calcule os limites:
(a) lim
x→0
tg x
x
(b) lim
x→0
x
sen x
(c) lim
x→0
sen 3x
x
(d) lim
x→pi
sen x
x− pi
(e) lim
x→0
x2
sen x
(f) lim
x→0
3x2
tg x sen x
(g) lim
x→0
tg 3x
sen 4x
(h) lim
x→0
1− cos x
x
(i) lim
x→pi
2
1− sen x
2x− pi
(j) lim
x→0 x sen
1
x
(k) lim
x→c
tg (x− c)
x2 − c2
, c 6= 0 (l) lim
x→c
sen (x2 − c2)
x− c
(m) lim
x→0
sen (x2 + 1
x
) − sen 1
x
x
(n) lim
x→0
x+ sen x
x2 − sen x
(o) lim
x→0
x− tg x
x+ tg x
(p) lim
x→1
sen pix
x− 1
(q) lim
x→0
x− sen x
x2
(r) lim
x→c
sen x− sen c
x− c
(s) lim
x→c
sec x− sec c
x− c
(t) lim
x→0+
sen x
x3 − x2
(u) lim
u→0+
√
u
tgu
(v) lim
x→0+
sen x√
x
(w) lim
t→0+
t√
tg t
(x) lim
t→0
t cos t
tg t
(y) lim
t→0+
tg t2
sen t3
(z) lim
u→0
u2 − 3senu2
tg 2u
2. 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 / INMA Turmas 1, 2, 3 e 7