   Chapter 3.10, Problem 30E ### 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

# Explain, in terms of linear approximations or differentials, why the approximation is reasonable.30. 4.02 ≈ 2.005

To determine

To explain: The linear approximation is reasonable.

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 4.02 by using linearization.

Since 4 is near integer of the value 4.02, choose the value a=4 and the function f(x)=x.

The linearization of the function f(x)=x at a=4 is computed as follows,

Consider f(x)=x,

Differentiate with respect to x,

f(x)=ddx(x)=12x121=12x12=12x

Substitute x=4,

f(0)=124=14

Substitute x=4 in f(x)=x, f(4)=2

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