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# Limites - Parte 2

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Ca´lculo I - Lista de Exerc´\u131cios no¯ 6 - 1o¯ semestre/2015
1. Calcule os limites:
(a) lim
x\u21920
tg x
x
(b) lim
x\u21920
x
sen x
(c) lim
x\u21920
sen 3x
x
(d) lim
x\u2192pi
sen x
x\u2212 pi
(e) lim
x\u21920
x2
sen x
(f) lim
x\u21920
3x2
tg x sen x
(g) lim
x\u21920
tg 3x
sen 4x
(h) lim
x\u21920
1\u2212 cos x
x
(i) lim
x\u2192pi
2
1\u2212 sen x
2x\u2212 pi
(j) lim
x\u21920 x sen
1
x
(k) lim
x\u2192c
tg (x\u2212 c)
x2 \u2212 c2
, c 6= 0 (l) lim
x\u2192c
sen (x2 \u2212 c2)
x\u2212 c
(m) lim
x\u21920
sen (x2 + 1
x
) \u2212 sen 1
x
x
(n) lim
x\u21920
x+ sen x
x2 \u2212 sen x
(o) lim
x\u21920
x\u2212 tg x
x+ tg x
(p) lim
x\u21921
sen pix
x\u2212 1
(q) lim
x\u21920
x\u2212 sen x
x2
(r) lim
x\u2192c
sen x\u2212 sen c
x\u2212 c
(s) lim
x\u2192c
sec x\u2212 sec c
x\u2212 c
(t) lim
x\u21920+
sen x
x3 \u2212 x2
(u) lim
u\u21920+
\u221a
u
tgu
(v) lim
x\u21920+
sen x\u221a
x
(w) lim
t\u21920+
t\u221a
tg t
(x) lim
t\u21920
t cos t
tg t
(y) lim
t\u21920+
tg t2
sen t3
(z) lim
u\u21920
u2 \u2212 3senu2
tg 2u
2. Calcule os limites:
(a) lim
x\u2192+\u221e 3x (b) limx\u2192\u2212\u221e 7x (c) limx\u2192\u2212\u221e ex
(d) lim
x\u2192+\u221e(0, 16)x (e) limx\u2192+\u221e(2x \u2212 3x) (f) limx\u2192+\u221e
1\u2212 2x
1\u2212 3x
(g) lim
x\u2192+\u221e 2\u2212x (h) limx\u2192\u2212\u221e 2\u2212x (i) limx\u2192+\u221e(2x + 2\u2212x)
(j) lim
x\u2192+\u221e log3 x (k) limx\u21920+ log 13 x (l) limx\u21920+ ln x
(m) lim
x\u2192+\u221e ln
x
x+ 1
(n) lim
x\u2192+\u221e[ln(2x+ 1) \u2212 ln(x+ 3)] (o) limx\u21921 ln
x2 \u2212 1
x\u2212 1
(p) lim
x\u2192+\u221e
(
1+
2
x
)x
(q) lim
x\u2192+\u221e
(
1+
1
x
)x+2
(r) lim
x\u2192+\u221e
(
1+
1
2x
)x
(s) lim
x\u2192+\u221e
(
1+
2
x
)x+1
(t) lim
x\u2192+\u221e
(
x+ 2
x+ 1
)x
(u) lim
x\u21920(1+ 2x)x
(v) lim
x\u21920(1+ 2x)
1
x (w) lim
x\u2192+\u221e
(
1+
1
x
)2x
(x) lim
x\u21920
e2x \u2212 1
x
(y) lim
x\u21920
ex
2
\u2212 1
x
(z) lim
x\u21920
5x \u2212 1
x
UFMS / INMA Turmas 1, 2, 3 e 7