How to compute the limit,$\lim_{x\rightarrow 0}\frac{3x^2-3x\sin x}{x^2+x\cos1/x}$ How to compute the limit,
$$\lim_{x\rightarrow 0}\frac{3x^2-3x\sin x}{x^2+x\cos\frac{1}{x}}$$

For any $\delta > 0$ there exists an $0<x<\delta$ such that $x - \cos \frac {1}{x} = 0$
As $x-\cos \frac 1x$ is continuous, the are points close to these zeros such that $ x-\cos \frac 1x $ is arbitrarily close to zero, and $\frac {3x^2 - 3x\sin x}{x(x-\cos \frac 1x)}$ is arbitrarily large.
