   Chapter 3.10, Problem 27E ### 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 linear approximation (or differentials) to estimate the given number.27. e0.1

To determine

To estimate: The value of e0.1 by using linear approximation.

Explanation

Result used:

The linear approximation of the function at x=a is L(x)=f(a)+f(a)(xa).

Calculation:

Obtain the value of e0.1.

Since 0 is near integer of the value 0.1, choose the value a=0 and the function f(x)=ex.

The linearization of the function f(x)=ex at a=0 is computed as follows,

Consider the function f(x)=ex,

Differentiate with respect to x,

f(x)=ddx(ex)=ex

Substitute x=0 in f(x),

f(0)=e0=1

Thus, the value of f(0)=1.

Substitute x=0 in f(x)=ex, f(0)=1

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