Question

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

• A. $2\sin 2$
• B. $2\tan 2$
• C. $\sin 2$
• D. $2\cos 2$

Answer 1

The correct option is A $2\sin 2$

$\underset{x\to -1}{lim}\frac{\cos 2-\cos 2x}{x^2-\left|x\right|}=l$ (say ) [is of the form $\frac{0}{0}$]

$l=\underset{x\to -1}{lim}\frac{0+\left(\sin 2x\right)\left(2\right)}{2x+1}(\because x\to -1,|x|=-x)$ [L' Hospital rule]

$l=\frac{2\sin (-2)}{-2+1}$

$l=2\sin 2$