   Chapter 3.2, Problem 29E

Chapter
Section
Textbook Problem

# Show that sin x < x   if  0 < x < 2 π .

To determine

To show:

sinx<x if 0<x<2π

Explanation

1) Concept:

We simplify using the Mean Value Theorem

2) Theorem:

Mean value theorem: If f be the function that satisfies

1) f is continuous on [a,b]

2) f is differentiable on (a,b)

Then, there is number c in [a,b] such that

f'c=fb-f(a)b-a

3) Calculation:

fx=sinx, is continuous and differentiable over R

Let x be any number such that 0<x<2π

By mean value theorem, there is a number c in (0,a) such that

fx-f0=f'(c)(x-0)

sinx-sin0=f'(c)x

f'c=ddx

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