- #1

- 69

- 14

## Homework Statement:

- Prove that ##x^2##/2>xcosx-sinx for all x≠0

## Relevant Equations:

- -

What I wanted to do was set f(x)=##x^2##/2 - xcosx+sinx And show that f(x)>0.

f'(x)=x(1+sinx)

First I wanted to prove that f(x)<0 in the interval (0,∞)

0≤1+sinx≤2

And thus for all x> 0 f'(x)≥0 and therefore f(x)≥f(0)=0

And it doesn't help me much because I need to f(x)>0

f'(x)=x(1+sinx)

First I wanted to prove that f(x)<0 in the interval (0,∞)

0≤1+sinx≤2

And thus for all x> 0 f'(x)≥0 and therefore f(x)≥f(0)=0

And it doesn't help me much because I need to f(x)>0