Evaluate the following limits $ \lim\limits_{ x \to 0} \large\frac{ ax + x\cos\: x}{b\sin \: x}$

Question

$\begin{array}{1 1}\frac{a+1}{b} \\ \frac{a}{b} \\ \frac{a+1}{b+1} \\ \frac{a}{1+b}\end{array} $