   Chapter 2.9, Problem 26E

Chapter
Section
Textbook Problem

# 23-28 Use a linear approximation (or differentials) to estimate the given number. 100.5

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=x ,  x = 100 and x= 0.5

2) Given: 100.5

3) Calculation:

Let fx=x ,  x = 100 and x= 0.5

Substitute x = 100 &x= 0.5 in  fx+x   fx+ f'xx

f100+0.5   f100+ f'100(0

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