# Draw a graph of xcos(1/x)

1. May 8, 2014

### JamesBwoii

1. The problem statement, all variables and given/known data
Draw a graph of xcos(1/x)

2. The attempt at a solution

I've differentiated the equation using the product rule.

This got me to:

cos(1/x) + sin(1/x)/x

What I don't know how to do is actually go about drawing the graph. This is also a past paper question for an exam where I won't be allowed calculators.

Thanks!

2. May 8, 2014

### pasmith

(1) $-x \leq x\cos(1/x) \leq x$.
(2) $\cos(1/x) \to 1$ as $x \to \infty$.
(3) How fast does $\cos(1/x)$ oscillate at $x \to 0$?