Download Calculus II Practice Exercises

Calculus II
Practice Exercises
Integral Test
Use the integral test to determine whether the series converges.
∞
1
1) ∑
8n
n=1
A) converges
∞
2)
∑
7
n
n=1
A) diverges
∞
3)
∑
∞
∑
∞
∑
∞
∑
∞
∑
B) diverges
cos 1/n
n2
n=1
A) converges
7)
B) converges
1
2n
e - 1
n=1
A) converges
6)
B) converges
1
2n - 1
n=1
A) diverges
5)
B) converges
7
n
n=1
A) diverges
4)
B) diverges
B) diverges
5n
2
n + 2
n=1
A) converges
B) diverges
Provide an appropriate response.
8) Which of the following is not a condition for applying the integral test to the sequence { a n }, where a n = f(n)?
I. f(x) is everywhere positive
II. f(x) is decreasing for x ≥ N
III. f(x) is continuous for x ≥ N
A) I only
B) II only
C) All of these are conditions for applying the integral test.
D) III only
9) Which of the following statements is false?
A) If a n and f(n) satisfy the requirements of the Integral Test, and if ∫
1
∫
∞
f(x) dx.
1
B) The integral test does not apply to divergent sequences.
∞
1
C) ∑
converges if p >1 and diverges if p ≤ 1.
np
n=1
∞
1
converges if p > 1.
D) ∑
n(ln n)p
n=2
∞
∞
f(x)dx converges, then ∑
n=1
a n =
Answer Key
Testname: 20_EX
1)
2)
3)
4)
5)
6)
7)
8)
9)
A
A
A
A
A
A
B
A
A