   Chapter 8.8, Problem 82E

Chapter
Section
Textbook Problem

True or False? In Exercises 81–86, determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.If f is continuous on [0, ∞ ) and ∫ 0 ∞ f ( x ) dx diverges, then lim x → ∞   f ( x )  ≠  0 .

To determine
Whether the statement “If f is continuous on [0,) and 0f(x)dx diverges, then limxf(x)0.” is true or false.

Explanation

Consider a function, f(x)=1x+1

This function is continuous on [0,).

Now, test for convergence:

limb0b1x+1=limb[ln|x+1|]0b=lim

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