MAC 2312 - Summer 2013
Homework #2 (Lectures 10-16)
Integration Strategies
Z
1.
x4
9xdx
+ x2 + 4
Z
√
5 9 + ex dx
Z
7x ln xdx
√
x2 − 16
Z
dt
sin t + cos(2t)
2.
3.
4.
2
Z
x sin x
dx
cos3 x
Z
sec6 x
dx1
tan2 x
5.
6.
Limits and L’Hospital’s Rule
7. lim
t→0
1
1
− 2
t t +t
8. lim ln(3x2 + 5) − ln(x2 − 5)
x→∞
p
9. lim x + x2 + 2x
x→−∞
10. lim (1 + x)1/x
x→0
11. lim arctan(x2 − x4 )
x→∞
12. lim
x→0
tan x − x
x3
Improper Integrals
Z
∞
7x arctan x
dx
(1 + x2 )2
∞
ln x
dx
x3
13.
0
Z
14.
1
Z
∞
1
dx
2
−∞ 1 + x
Z ∞
16.
e−|x| dx
15.
−∞
Sequences
Determine whether the sequence converges or diverges. If it converges, find its limit.
17. an =
(2n − 1)!
(2n + 1)!
18. an =
cos2 n
2n
19. an = n2 e−n
20. an =
7n!
3n
21. an =
en + e−n
e2n − 1
MAC 2312 - Summer 2013
Homework #2 (Lectures 10-16)
2 1/n
22. an = 1 +
n
23. an =
5n + 3n−1
8n
Series
Determine whether the series converges or diverges. If it is convergent, find the sum.
24.
∞
X
cosk 1
n=1
25.
∞
X
1 + 5n
n=1
26.
8n
∞
X
3
2
−
n
5
n
n=1
27.
∞
X
(−3)n−1
n=2
28.
∞
X
n=1
4n
arctan n