   Chapter 4.4, Problem 25E ### 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 − 4 x x

To determine

To evaluate: The value of   limx01+2x14xx .

Explanation

Obtain the value of the function as x approaches 0 .

As x approaches 0 , the numerator is,

1+2x14x=1+2(0)14(0)=1+010=11=0

As x approaches 0 , the denominator x is also 0 .

Thus, limx01+2x14xx=00 is in an indeterminate form.

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

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