Sample Calculus II Questions

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... see moreat least 80%. If you feel that you would need more than a little review, then you ought to enroll in Math 126.
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5) Which of the following improper integrals converge?

(b)

(c)

(d)

(a)

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.

Explanation

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