   Chapter 4.4, Problem 59E ### 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   ( 1 − 2 x ) 1 / x

To determine

To evaluate: The value of limx0(12x)1x .

Explanation

Let y=limx0(12x)1x (1)

Take natural logarithm on both sides,

lny=ln(limx0(12x)1x)=limx0(ln(12x)1x)=limx0(1xln(12x))=limx0ln(12x)x

Therefore lny=limx0ln(12x)x . (2)

Obtain the value of the function as x approaches 0 .

As x approaches 0 , the numerator is,

ln(12x)=ln(10)=ln(1)=0

As x approaches 0 , the denominator is, x=0

Thus, limx0ln(12x)x=00 is in an indeterminate form

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