revisao P1 Calculo 1

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MAT 140 - Ca´lculo I Revisa˜o P1-1
I. Calcule os seguintes limites, caso existam.
1. lim
x→2
[
(x2 − 5x+ 6)sen
(
2x− 5
x+ 6
)]
6. lim
t→p
[
4
√
t− 4√p
x− p
]
11. lim
x→+∞
2x+ 3
x− 3√x
2. lim
x→2
[
(x2 − 5x+ 6)sen
(
x2 − 5
x− 2
)]
7. lim
x→0
( |x| − 1
|x− 1|
)
12. lim
x→−∞
x− 3√1− x3
3. lim
x→a
(
x2 + (b− a)x− ab
x2 + (1− a)x− a
)
8. lim
x→1
∣∣∣∣x2 − 4x+ 10x2 − 2x+ 1
∣∣∣∣ 13. limx→+∞ (2x+ 3)3(3x− 2)2(x+ 4)5
4. lim
u→−2
[
u3 + 4u2 + 4u
u2 − u− 6
]
9. lim
x→pi
2
sen(2x)
x− pi
2
14. lim
x→−∞
x
√−x√
1− 4x2
5. lim
t→p
[
3
√
t− 3√p
t− p
]
10. lim
x→+∞
x+ sen(x)
x+ cos(x)
15. lim
x→4−
√
16− x2
x− 4
II. Estude a continuidade das func¸o˜es abaixo.
1. f(x) =

x2−9
x−3 , se x 6= 3
5, se x = 3
4. f(x) =

x2 − 9
x− 3 , se x < 3
Ax2 +B, se 3 ≤ x < 7
2. f(x) =

x2−9
x−3 , se x < 3
x2 − 9, se 3 ≤ x < 7
x+ 5, se x ≥ 7
5. f(x) =

A(x+ 1)2 +B, se x < −1
−|x|+ 1, se − 1 ≤ x < 1
A(x− 2)2 +B, se x ≥ 1
3. f(x) =

−|x+ 4|+ 6, se x < −4
√
25− x2 + 1, se − 4 ≤ x < 4
−|x− 4|+ 6, se x ≥ 4
6. f(x) =

A|x+ 4|+B, se x < −4
√
25− x2 + 1, se − 4 ≤ x < 4
A|x− 4|+B, se x ≥ 4
1
III. Determine as assintotas das curvas:
1. y =
x2 + 9
(x− 3)2 2. y =
x2 + 2x− 1
x
3. y = 3− 2x− x
2
√
x2 − x− 2
4. x2(x+ y) = a2(x− y) 5. x2(x− y)2 − a2(x2 + y2) = 0 6. y = x
2
√
x2 − 1
IV. Calcule as duas primeiras derivadas de:
1. y =
cos(x)
x2
+
1 + x2
1− x2 2.y = sec(x) 3. y = tan(x)
4. y = sen(x)[x5 +
ex
x2 − 1] 5. y =
sen(x) + cos(x)
sen(x)− cos(x) 6. y = x
2(x3 −√x)(sen(x)− tan(x)))
2