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## Homework Statement

I am attempting to show that [itex]-x \leq sin(x) \leq x[/itex] for x>0 and thus [itex]\int^1_0 nxsin(\frac{1}{nx})dx[/itex] converges to 1.

## Homework Equations

I know that I need to use the fact that I have shown that the limit as T tends to infinity of [itex]\int^T_1 \frac{cos(x)}{\sqrt{x}}dx[/itex] exists.