Mathematics - Limits Question with Solution | TestHub

The given limit can be written as:

$$\underset{x\to 0}{\lim }\left(\frac{\sin nx}{nx}\right)(n)\left((a-n)n-\frac{\tan x}{x}\right)=0$$

This implies:

$$(1)(n)((a-n)n-1)=0$$

Since $n\ne 0$, we have:

$$(a-n)n-1=0$$

Solving for $a$:

$$a=n+\frac{1}{n}$$