   Chapter 4.4, Problem 87E ### 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

# If f′ is continuous, f(2) = 0, and f′(2) = 7, evaluate lim x → 0 f ( 2 + 3 x ) + f ( 2 + 5 x ) x

To determine

To evaluate: The value of limx0f(2+3x)+f(2+5x)x .

Explanation

Given:

For the function f , it is given that f(2)=0 and f(2)=7 .

Calculation:

Obtain the value of the function as x approaches 0 .

As x approaches 0 , the numerator is

f(2+3x)+f(2+5x)=f(2)+f(2)=0+0=0

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

Thus, limx0f(2+3x)+f(2+5x)x=00 is in an indeterminate form

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