JEE Math Practice Question

Let $f, g$ and $h$ be the real valued functions defined on $\mathbb{R}$ as $f(x)=\left\{\begin{array}{cc}\frac{x}{|x|}, & x \neq 0 \\ 1, & x=0\end{array}\right.$ $g(x)=\left\{\begin{array}{cc}\frac{\sin (x+1)}{(x+1)}, & x \neq-1 \\ 1, & x=-1\end{array}\right.$ and $h(x)=2[x]-f(x)$, where $[x]$ is the greatest integer $\leq x$. Then the value of $\lim\limits_{x \rightarrow 1} g(h(x-1))$ is :

1. A.1
2. B.$-1$
3. C.$\sin (1)$
4. D.0