Question

If $\underset{x\to 0}{lim}\frac{\left(\right(a-n)nx-\tan x)\sin nx}{x^2}=0$ where n is nonzero real number, then a is equal to

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

$\underset{x\to 0}{lim}\frac{\left(\right(a-n)nx-\tan x)\sin nx}{x^2}=0$
$\underset{x\to 0}{lim}\left(\right(a-n)n-\left(\frac{\tan x}{x}\right)).\frac{\sin nx}{nx}.n=0$
$\Rightarrow \left(\right(a-n)n-1).1.n=0$
$\Rightarrow a=\frac{1}{n}+n$