   Chapter 3.10, Problem 31E

Chapter
Section
Textbook Problem

Explain, in terms of linear approximations or differentials, why the approximation is reasonable.31. 1 9.98 ≈ 0.1002

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 19.98 by using linearization.

Since 10 is near integer of the value 9.98, choose the value a=10 and the function f(x)=1x.

The linearization of the function f(x)=1x at a=10 is computed as follows,

Consider f(x)=1x,

Differentiate with respect to x,

f(x)=ddx(1x)=1x2=1x2

Substitute x=10,

f(10)=1102=1100

Substitute x=10 in f(x)=1x, f(10)=110

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