Let \( f, g \) and \( h \) be the real valued function defined on \( R \) as \( f(x)=\left\{\beg....

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Let \( f, g \) and \( h \) be the real valued function defined on
\( \mathrm{P} \)
\( R \) as \( f(x)=\left\{\begin{array}{cc}\frac{x}{|x|}, & x \neq 0 \\ 1, & x=0\end{array}\right. \)
\[
g(x)=\left\{\begin{array}{cc}
\frac{\sin (x+1)}{|x|}, & x \neq-1 \\
1, & x=-1
\end{array}\right.
\]
W.
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) -1
(3) \( \sin (1) \)
(4) 0


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