Question

Find the following limits (424-425)
$\underset{x\to -1}{lim}\frac{cos2-cos2x}{x^2-|x|}$

Answer 1

$\underset{x\to -1}{lim}\frac{\cos 2-\cos 2x}{x^2-\left|x\right|}$ $\left|x\right|=\{x,x>0-x,x<0\}$

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

$=\underset{x\to -1}{lim}\frac{\sin 2x.2}{2x+1}$ {Applying L.Hospital}

$=\frac{-2\sin 2}{-1}=2\sin 2$