Lista 1 CI F 2016 1

Prévia do material em texto

.
Universidade Federal do Piau´ı - UFPI
Departamento de Matema´tica
Lista 1: Ca´lculo I - F
Prof. C´ıcero Aquino
1. Use a definic¸a˜o para verificar que
(a) lim
x→xo
(ax+ b) = axo + b (b) lim
x→xo
√
x =
√
xo
2. Calcule, caso existam, os seguintes limites
(a) lim
x→3
x2 − 9
x− 3
(b) lim
x→1
1−√x
1− x
(c) lim
x→9
9− x
3−√x
(d) lim
x→1
√
x− x2
1−√x
(e) lim
x→9
x2 − 81√
x− 3
(f) lim
x→1
x3 − 1
x2 − 1
(g) lim
x→4
√
x− 2
x− 4
(h) lim
x→8
3
√
x− 2
x− 8
(i) lim
x→16
4
√
x− 2
x− 16
3. Calcule, caso existam, os seguintes limites
(a) lim
x→2
x2 + x− 6
x− 2
(b) lim
x→0
(4 + x)2 − 16
x
(c) lim
x→0
(2 + x)3 − 8
x
(d) lim
x→0
√
1 + x− 1
x
(e) lim
x→7
√
x+ 2− 3
x− 7
(f) lim
x→0
(
1
x
√
x+ 1
− 1
x
)
(g) lim
x→0
(
1
x
− 1
x2 + x
)
(h) lim
x→0
√
3 + x−√3
x
(i) lim
x→2
√
6− x− 2√
3− x− 1
4. Calcule, caso existam, os seguintes limites
(a) lim
x→1−
|x2 − x|
x− 1
(b) lim
x→−4+
|x+ 4|
x+ 4
(c) lim
x→0+
(
1
x
− 1|x|
)
(d) lim
x→1−
x2 − 1
|x− 1|
(e) lim
x→2+
x− 2
|x− 2|
(f) lim
x→3−
|x2 − 9|
x− 3
(g) lim
x→−3−
x+ 3√
(x+ 3)2
(h) lim
x→2+
4− x2
2− x
(i) lim
x→pi−
|pi − x|
x− pi
5. Calcule, caso existam, os seguintes limites
(a) lim
x→+∞
√
2x+ 1
3x− 5
(b) lim
x→0+
lnx
(c) lim
x→−∞
ex
(d) lim
x→+∞
1
x3
(e) lim
x→−∞
1
x2 + 3
(f) lim
x→1−
1
x2 − 1
(g) lim
x→−∞
arctg x
(h) lim
x→+∞
3x4 − 3x2 + 2
2x4 + 2x+ 1
(i) lim
x→−∞
x2 − 2
x3 + 1
Semestre: 2016-1 -1- Data: 16/04/2016
6. Calcule, caso existam, os seguintes limites
(a) lim
x→1
1
(x− 1)3
(b) lim
x→0+
1
lnx
(c) lim
x→+∞
(
√
x+ 2−√x)
(d) lim
x→+∞
− 2x
(x3 − 1)2
(e) lim
x→+∞
sen x
x
(f) lim
x→−∞
x+ 2√
x2 + 1
(g) lim
x→−∞
√
9x6 − x
x3 + 1
(h) lim
x→+∞
(x−√x)
(i) lim
x→−∞
x3 − 2x
1− x2
7. Calcule, caso existam, os seguintes limites
(a) lim
x→0
2 + senx
3 + x
(b) lim
x→0
1− cos 3x
x
(c) lim
x→0
4x2 + 3xsenx
x2
(d) lim
x→0
x cos x− x2
2x
(e) lim
x→0
cossec 2x
cotg 3x
(f) lim
x→0
sen2 2x
x2
(g) lim
x→0
x+ tgx
senx
(h) lim
x→0
sen 3x
sen 4x
(i) lim
x→0
sen x
3
√
x
(j) lim
x→0
x2cossec2 x
(k) lim
x→0
sen (x/3)
x
(l) lim
x→0
1− 2 cos x− cos2 x
x2
8. Considere a func¸a˜o f : [−3, 3]→ R definida por
f(x) =

a , se x = −3
9− x2
4−√x2 + 7 , se |x| < 3
b , se x = 3
Encontre os valores de a e b que tornam f uma func¸a˜o cont´ınua.
Semestre: 2016-1 -2- Data: 16/04/2016