   Chapter 2, Problem 11RQ ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### 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 p is a polynomial, then lim x → b p ( x ) = p ( b ) .

To determine

Whether the statement, “If p is a polynomial, then limxbp(x)=p(b)” is true or false.

Explanation

Definition used: “A function f is continuous at a number a if limxaf(x)=f(a)”.

Theorem used: “Any polynomial is continuous everywhere; that is, it is continuous on =(,)”.

Reason:

Let p(x) be a polynomial defined in .

By Theorem 5, the polynomial p is continuous everywhere. So it is continuous at b

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