Let $f$, $g$ and $h$ be the real valued functions defined on $\mathbb{R}$ as\\
$f(x) = \left\{ \begin{array}{cc} \frac{x}{|x|}, & x \neq 0 \\ 1, & x = 0 \end{array} \right.$, $\quad g(x) = \left\{ \begin{array}{cc} \frac{\sin(x+1)}{(x+1)}, & x \neq -1 \\ 1, & x = -1 \end{array} \right.$ and $h(x) = 2[x] - f(x)$, where $[x]$ is the greatest integer $\leq x$. Then the value of $\lim_{x \rightarrow 1} g(h(x-1))$ is\\
(1) 1\\
(2) $\sin(1)$\\
(3) $-1$\\
(4) 0