Question

$\underset{x\to -1}{lim}\frac{cos2-cos2x}{x^2-|x|}$ is equal to

• A. $2$
• B. $sin2$
• C. $2sin2$
• D. None of these

Answer 1

The correct option is C $2sin2$

We have,
$\underset{x\to -1}{lim}\frac{cos2-cos2x}{x^2-|x|}$
$=\underset{x\to -1}{lim}\frac{2sin(1+x)sin(x-1)}{x^2+x}$
$[\because |x|=-xforx<0]$
$=2\underset{x\to -1}{lim}\frac{sin(x+1)}{x+1}\times \frac{sin(x-1)}{x}$
$=2\times 1\times \frac{sin(-2)}{(-1)}=2sin2$
Hence, option 'C' is correct.