Cálculo Diferencial I Lista complementar

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UNIVERSIDADE DA INTEGRAC¸A˜O INTERNACIONAL DA LUSOFONIA
AFRO-BRASILEIRA
INSTITUTO DE CIEˆNCIAS EXATAS E DA NATUREZA
CURSO DE LICENCIATURA PLENA EMMATEMA´TICA
Lista complementar de Ca´lculo Diferencial I.
Professor: Rafael Dio´genes.
Aluno:
1. Calcule o limite, caso exista.
(a) lim
x→0
sen 3x
2x
(b) lim
x→0
sen 2x
senx
(c) lim
x→0
tg 2x
3x
(d) lim
x→0
tg x+ senx
x
(e) lim
x→0
1− cosx
xsenx
(f) lim
x→a
senx− sen a
x− a
(g) lim
x→a
cosx− cos a
x− a
(h) lim
x→0
xsen
1
x
(i) lim
x→+∞
xsen
1
x
(j) lim
x→+∞
(
1 +
1
x
)x+2
(k) lim
x→+∞
(
1 +
2
x
)3x
(l) lim
x→+∞
(
1 +
3
x
)x
4
(m) lim
x→+∞
(
x+ 4
x− 3
)x
(n) lim
x→+∞
(
x− 4
x− 1
)x+3
(o) lim
x→+∞
(
x2 + 1
x2 − 3
)x2
(p) lim
x→0
23x − 1
x
(q) lim
x→0
22x − 1
e5x − 1
(r) lim
x→0
e2x − 1
e3x − 1
(s) lim
x→a
2x − 2a
x− a
(t) lim
x→0
ln(1 + x)
x
(u) lim
x→0
log(1 + x)
x
(v) lim
x→0
ln(1 + 2x)
x
(w) lim
x→0
ln(1 + 3x)
x
(x) lim
x→0
ln(1 + x)3
x
(y) lim
x→0
ln(1 + 4x)2
x
(z) lim
x→0
x
√
1− 2x
“So´ Deus e´ dono da vida.”
(Sa˜o Joa˜o Paulo II)