Chapter 7: Q.1.a) (page 630)
If for every x0 and the improper integralconverges, then the improper integral converges. The objective is to whether determine the statement is true or false
Short Answer
True
Chapter 7: Q.1.a) (page 630)
If for every x0 and the improper integralconverges, then the improper integral converges. The objective is to whether determine the statement is true or false
True
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Get started for freeIn Exercises 48–51 find all values of p so that the series converges.
Let f(x) be a function that is continuous, positive, and decreasing on the interval such that role="math" localid="1649081384626" . What can the divergence test tell us about the series ?
If a positive finite number, what may we conclude about the two series?
Given a series , in general the divergence test is inconclusive when . For a geometric series, however, if the limit of the terms of the series is zero, the series converges. Explain why.
Let be a continuous, positive, and decreasing function. Complete the proof of the integral test (Theorem 7.28) by showing that if the improper integral converges, then the series localid="1649180069308" does too.
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