These Statements are false, please provide an explicit counterexample: a) If f(x) is a continuous, always positive function on (1,20) and lim F(x) = 0 then S, f(x)dx will converge. b) It an is an always positive sequence and diverges then an∞.

These Statements are false, please provide an explicit counterexample: a) If f(x) is a continuous, always positive function on (1,20) and lim F(x) = 0 then S, f(x)dx will converge. b) It an is an always positive sequence and diverges then an∞.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter6: Applications Of The Derivative

Section6.CR: Chapter 6 Review

Problem 1CR

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These Statements are false, please provide an explicit counterexample:
a) If f(x) is a continuous, always positive function on (1,20) and
lim F(x) = 0 then S, f(x)dx will converge.
b) It an is an always positive sequence and diverges
then an∞.

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