   Chapter 2.9, Problem 28E

Chapter
Section
Textbook Problem

# 23-28 Use a linear approximation (or differentials) to estimate the given number. cos 29 °

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

iv. Let fx=cosx , x=300 & x= -10

2) Given: cos290

3) Calculation:

Substitute x=300 & x= -10 in  fx+x   fx+ f'xx

f300-10   f300+ f'300(-10)

f290   f300+ f'300(-10)

To find  f300, substitute x=300  in fx=cosx

f300=cos300 =32

To find  f'(300), find derivative of f(x)

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