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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621

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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621
Textbook Problem

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

1 / 4.002

To determine

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

Explanation

1) Formula:

i. Limit definition of differentiation:

a. f'x= limx0fx+x-fxx

ii. For small values of ∆x,

a. f'x fx+x-fxx

b. f'xx  fx+x-fx

c.  fx+x   fx+ f'xx

iii. Power rule of derivative:

a. ddxxn=n xn-1

iv. fx=1x , x = 4 and x= 0.002

2) Given:

14.002

3) Calculation:

Let fx=1x , x = 4 and x= 0.002

Substitute x = 4 &x= 0.002 in  fx+x   fx+ f'xx

 f4+0.002   f4+ f'4(0

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