Question

$\underset{x\to 0}{lim}\frac{ax+x\cos x}{b\sin x}$

Answer 1

$\underset{x\to 0}{lim}\frac{ax}{b\sin x}+\frac{x\cos x}{b\sin x}$

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

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

$[\because \underset{x\to 0}{lim}\frac{x}{\sin x}-1]$.