Problem 10
Match the following improper integral with the improper integral below in which you can compare using the Comparison Test. Then determine whether the integral converge or diverge.
A. , B. , C. , and D.
1. , Answer: B, Converges.
Key step:
2. , 'Answer: D, Diverges.
Key step:
, so
3. , 'Answer: A, Diverges.
Key step:
When the denominator is decreased, the fraction increases. So
4. , 'Answer: A, Diverges.
Key step:
Recall the range of is [-1,1], so