   Chapter 4.4, Problem 7E ### 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

# The graph of a function f and its tangent line at 0 are shown. What is the value of lim x → 0   f ( x ) e x − 1 ? To determine

To evaluate: The value of limx0f(x)ex1 by using graph of f .

Explanation

Result used:

L’Hospital’s rule: For differentiable functions f and g where g0 and if the limit limxaf(x)g(x) is in indeterminate form then, limxaf(x)g(x)=limxaf(x)g(x) .

Given:

From the graph it can be identified that the equation of the tangent line of the graph f is y=x .

Calculation:

From the graph, line y=x is tangent to the curve f . So,  it represents first derivative of f.

Thus f(x)=1

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