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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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Chapter
Section
BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.

If f'(r) exists, then lim x r f ( x ) = f ( r ) .

To determine

Whether the statement, “if f(r) exists, then limxrf(x)=f(r)” is true or false.

Explanation

Definition used:

A function f is continuous at a number a if and only if limxaf(x)=f(a).

Theorem used: If f is differentiable at a, then f is continuous at a.

Reason:

Given that f(r) exists

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