Which of the following improper integrals converge?

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Questions: 5 | Attempts: 903 | Updated: Aug 14, 2024

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A student need not get 100% on the questions below in order to skip Calculus II (Math 126) and go straight into Linear Algebra (Math 220). An initial score of at least 50% is good enough as long as you feelthat a little review would bring your score up to at least 80%. If you feel that you would need more than a little review, then you ought to enroll in Math 126.

Questions and Answers

1.

Use either substitution or integration-by-parts to find the following indefinite integral:
- A.
- B.
- C.
- D.
Correct Answer
A.
2.

Which of the following improper integrals converge?
- A.
  
  (b)
- B.
  
  (c)
- C.
  
  (d)
- D.
  
  (a)
Correct Answer(s)
A. (b)
C. (d)

Explanation
In order for an improper integral to converge, the limit of the integral as it approaches infinity or negative infinity must exist and be finite. In option (a), the integral does not converge as the limit of the integral as it approaches infinity does not exist. In option (b), the integral converges as the limit of the integral as it approaches infinity exists and is finite. In option (c), the integral does not converge as the limit of the integral as it approaches negative infinity does not exist. In option (d), the integral converges as the limit of the integral as it approaches negative infinity exists and is finite.

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2
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3.

Which of the following limits equals the sum of the series ?
- A.
- B.
- C.
- D.
Correct Answer
B.
4.

The Taylor series for about is: What is the interval of convergence of the Taylor series
- A.
- B.
- C.
- D.
Correct Answer
D.
5.

Compute the area bounded by the curves and .

Correct Answer
4