   Chapter 2, Problem 1RQ

Chapter
Section
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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