   Chapter 2.4, Problem 94E

Chapter
Section
Textbook Problem

In Exercises 89-94, determine whether the statement is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false.94. lim x → 1 ( 2 x x − 1 − 2 x − 1 ) = lim x → 1 2 x x − 1 − lim x → 1 2 x − 1

To determine
Whether the given statement “ limx1(2xx12x1)=limx12xx1limx22x1 ” is true or false.

Explanation

If f(x) and g(x) are two functions such that limit for both function exists as x tends to a. Then,

limxa(f(x)g(x))=limxaf(x)limxag(x)

The given function is limx1(2xx12x1) (1)

Simplify the above expression and apply the limit.

limx1(2xx12x1)=limx1(2x2x1)=limx12(x1x1

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