   Chapter 2, Problem 5RQ ### 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. lim x → 3 x 2 − 9 x − 3 = lim x → 3 ( x + 3 )

To determine

Whether the statement, limx3x29x3=limx3(x+3) is true or false.

Explanation

Fact 1: “If f(x)=g(x) when xa, then limxaf(x)=limxag(x), provided the limits exist”.

Calculation:

Let the function f(x)=x29x3 and g(x)=x+3.

Here, the function f(x) is undefined at x=3, but g(x) is defined.

That is, x29x3=x+3 is true whenever x3.

Apply fact 1 to check the limit exist are not.

limx3x29x3=limx3x232x<

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