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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336

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BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336
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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