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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 2, Problem 14RQ

To determine

Whether the statement, “If *f* is continuous on *r* such that

Expert Solution

The statement is false.

**Theorem used: The Intermediate value Theorem**

Suppose that if *f* is continuous on the closed interval [*a*, *b*] and let *N* be any number between *c* in (*a*, *b*) such that

**Reason:**

Suppose *f* is continuous on

Let

Then by Intermediate value theorem states that, there is a number *r* in the interval (−1, 1) such that

Thus, there is a number *r* such that

Therefore, the given statement is true.