   Chapter 2.2, Problem 27E

Chapter
Section
Textbook Problem

Use a table of Values to estimate i:he value of the limit. If you have a graphing device. use it to confirm your result graphically. lim x → 0 + x x

To determine

To evaluate: The value of limx0+xx.

Explanation

Since x approaches 0 from the right side, evaluate the function f(x)=xx for the numbers x=0.5,0.1,0.01,0.001,0.0001 and 0.00001 and obtain the following table of values.

 x f(x)=xx 0.5 0.707106 0.1 0.794328 0.001 0.954992 0.0001 0.993116 0.00001 0.999079 0.000001 0.999884

Here, it is observed that the value of f(x) gets closer to the largest positive value as x approaches to 0 from the right side.

That is, limx0+xx=1

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