   Chapter 2, Problem 1RQ ### 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 → 4 ( 2 x x − 4 − 8 x − 4 ) = lim x → 4 2 x x − 4 − lim x → 4 8 x − 4

To determine

Whether the statement, limx4(2xx48x4)=limx4(2xx4)limx4(8x4) is true or false.

Explanation

Difference law: Suppose that the limits limxaf(x) and limxag(x) exist.

Then limxa[f(x)g(x)]=limxaf(x)limxag(x).

Reason:

Let the function f(x)=2xx4 and g(x)=8x4.

Then, by the difference rule, the given statement is true only if the individual limits are exists.

That is, limx4(2xx48x4)=limx4(2xx4)limx4(

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Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 