Question

$\underset{x\to a}{lim}\frac{x\sin a-a\sin x}{x-a}=$

Answer 1

Now,

$\underset{x\to a}{lim}\frac{x\sin a-a\sin x}{x-a}$ $\left(\frac{0}{0}\right)$ form .

Now applying L'Hospital's rule we get,

$\underset{x\to a}{lim}\frac{\sin a-a\cos x}{1}$

$=\sin a-a\cos a$