   Chapter 4.4, Problem 61E ### 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 → 1 + x 1 / ( 1 − x )

To determine

To evaluate: The value of limx1+x11x .

Explanation

Given:

Let, y=limx1+x11x . (1)

Calculation:

Take natural logarithm on both sides,

lny=ln(limx1+x11x)=limx1+(lnx11x)=limx1+(11xln(x))=limx1+ln(x)1x

Therefore, lny=limx1+lnx1x . (2)

Obtain the value of the function as x approaches 1+ .

As x approaches 1+ , the numerator is,

lnx=ln1=0

As x approaches 1+ , the denominator is,

1x=11=0

Thus, limx1+lnx1x=00 is in an indeterminate form

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