Gabarito - Lista5-TurmasT01T50

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UNIVERSIDADE FEDERAL DE SERGIPE
DEPARTAMENTO DE MATEMA´TICA
Disciplina: Ca´lculo Diferencial e Integral I Turmas: T01 e T50
Prof.: Ana Cristina Salviano Veiga Data: 10/05/16
GABARITO - QUINTA LISTA DE EXERCI´CIOS
1. (a) ex
2
(b) xex (c) −√1 + sec x
(d) 6x5 cos10(x6) (e) −cos((lnx)
3)
x
+ senhx cos(cosh3 x)
2. 3
3. (a)
7
8
√
2arctg
(x− 2√
2
)
+
3x− 8
4x2 − 16x+ 24 + C
(b)
1
2
(x+ 1)
√
x2 + 2x− 1
2
ln |x+ 1 +
√
x2 + 2x|+ C
(c)−1
6
cos(3x)− 1
26
cos(13x) + C
(d)
1
8
sen(4x)− 1
12
sen(6x) + C
4. (a)
2
5
(b) − 1
270
(c) 4 (d) 2
√
3− 2
√
2 (e)
pi2
72
(f)
pi
12
+
√
3
2
− 1 (g) 117
8
(h)
22
√
2− 8
105
(i)
12
35
(j)
3
2
+ ln(
1
2
) (k)
pi
24
+
√
3
8
− 1
4
(l) — (m)
7
6
+ ln(
2
3
)
(n)
27
5
ln 2− 9
5
ln 3 (o)
√
2− 2√
3
+ ln(2 +
√
3)− ln(1 +
√
2)
5. (a)
4
3
(b) 18 (c) 4
6. (a)
47pi
210
(b)
41pi
105
7. (a)
27pi
2
(b)
625pi
6
8. (a)
pi
3
(b) −∞ (c) 3e
−2
4