   Chapter 2.9, Problem 27E

Chapter
Section
Textbook Problem

# 23-28 Use a linear approximation (or differentials) to estimate the given number. tan 2 °

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.

iv. Let fx=tanx , x= & x=

2) Given: tan

3) Calculation:

Let fx=tanx , x= & x=

Substitute x= and x= =π90 radian in  fx+x   fx+ f'xx

f+   f+ f'()

f

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