   Chapter 2.9, Problem 23E

Chapter
Section
Textbook Problem

# 23-28 Use a linear approximation (or differentials) to estimate the given number. ( 1.999 ) 4

To determine

To estimate: The given number by using a linear approximation (or differentials).

Explanation

1) Formula:

i. Limit definition of differentiation:

f'x= limx0fx+x-fxx

ii. For small values of ∆x,

f'x fx+x-fxx

f'xx  fx+x-fx

fx+x   fx+ f'xx

iii. Power rule of derivative:

ddxxn=n xn-1

iv. Let fx=x4,  x = 2 and x= - 0.001

2) Given:

1.9994

3) Calculation:

Let fx=x4,  x = 2 and x= - 0.001

Substitute x = 2 &x= -0.001 in  fx+x   fx+ f'xx

f2-0.001   f2+ f'2(-0

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