   Chapter 4.4, Problem 35E ### 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 ln ( 1 + x ) cos x + e x − 1

To determine

To evaluate: The value of limx0ln(1+x)cosx+ex1 .

Explanation

Obtain the value of the function as x approaches 0 .

As x approaches 0 , the numerator ln(1+x) approaches to 0 and denominator is,

cosx+ex1=cos0+e01=1+11=1

Since limx0ln(1+x)cosx+ex1 is not in an indeterminate form, L’Hospital’s Rule is not applicable

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