Question

If ${lim}_{x\to -1}\frac{\cos 2-\cos 2x}{x^2-\left|x\right|}$ is equal to -

Answer 1

$\underset{x\to -1}{lim}\frac{\cos 2-\cos 2x}{x^2-|x|}$

$=\underset{x\to -1}{lim}(\frac{\cos 2x-\cos 2}{x+1}.\frac{-1}{x})$

$=\underset{x\to -1}{lim}\frac{\cos 2x-\cos 2}{x+1}.\underset{x\to -1}{lim}\frac{-1}{x}$

$=2\sin 2.1$

$=2\sin 2$