   Chapter 4.4, Problem 70E ### 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

# Use a graph to estimate the value of the limit. Then use l’Hospital’s Rule to find the exact value. lim x → 0 5 x − 4 x 3 x − 2 x

To determine

To estimate: The value of limx05x4x3x2x using graph and then find the exact value of the same using L’Hospital’s rule.

Explanation

Use the online graphing calculator and draw the graph of 5x4x3x2x as shown below in Figure 1.

From Figure 1, it is identified that curve approaches approximately 0.55 as x approaches 0.

Find the exact value with the help of L’Hospital’s rule as follows.

Obtain the value of the function as x approaches 0 .

As x approaches 0 , the numerator is,

5x4x=5040=11=0

As x approaches 0 , the denominator is,

3x2x=3020=11=0 .

Thus, limx05x4x3x2x=00 is in an indeterminate form.

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

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