   Chapter 4.4, Problem 57E ### 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

# Find the limit. Use l’Hospital’s Rule where appropriate. If there is a more elementary method, consider using it. If l’Hospital’s Rule doesn’t apply, explain why. lim x → 0 + x x

To determine

To evaluate: The value of limx0+xx .

Explanation

Let y=limx0+xx . (1)

Take natural logarithm on both sides,

lny=ln(limx0+xx)=limx0+(lnxx)=limx0+(xlnx)

Express x as x=(x)2 ,

lny=limx0+(xln(x)2)=limx0+(2xln(x))=limx0+2ln(x)1x=limx0+2ln(1x)1x

Therefore lny=limx0+(2ln(1x)1x) (2)

Obtain the value of the function as x approaches 0+ .

As x approaches 0+ , the numerator is,

2ln(1x)=2ln(1x)=2ln(10)=

As x approaches 0+ , the denominator is,

1x=10=

Thus, limx0+2ln(1x)1x= is in an indeterminate form

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