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Chapter 8.8, Problem 82E
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### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

#### Solutions

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BuyFindarrow_forward

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
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,âˆž).

Now, test for convergence:

limbâ†’âˆžâˆ«0b1x+1=limbâ†’âˆž[ln|x+1|]0b=lim

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