   Chapter 4.4, Problem 15E ### 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 t → 0 e 2 t − 1 sin t

To determine

To evaluate: The value of limt0e2t1sint.

Explanation

Obtain the value of the function as t approaches 0.

As t approaches 0, the numerator is,

e2t1=e2(0)1=11=0

As t approaches 0, the denominator is,

sint=sin(0)=0

Thus, limt0e2t1sint=00 is in an indeterminate form.

Therefore, apply L’Hospital’s Rule and obtain the limit as shown below

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Study Guide for Stewart's Multivariable Calculus, 8th 