Consider, \( f(x)=\left[\begin{array}{cc}2-|x|, & -1 \leq x \leq 1 ...
Consider, \( f(x)=\left[\begin{array}{cc}2-|x|, & -1 \leq x \leq 1 \\ |x-2|-x, & 1x \leq 3\end{array}\right. \) and \( g(x)=\left[\begin{array}{cc}\sin x-1, & 0 \leq x\frac{\pi}{2} \\ {[x]-\cos (x-2),} & \frac{\pi}{2} \leq x \leq \pi\end{array}\right. \)
P
W where \( [k] \) denotes greatest integer function of \( k \). Identify the correct statement \( (s) \).
(a) \( \lim _{x \rightarrow 1^{+}} g(f(x))=-1 \)
(b) \( \lim _{x \rightarrow \frac{\pi^{-}}{2}} g(f\{g(x)\})=0 \)
(c) \( \lim _{x \rightarrow 2^{+}} \frac{f(g(x))}{f(x)-2}=\frac{1}{2} \)
(d) \( \lim _{x \rightarrow 0^{+}} \frac{g(f(x))}{(f(x)-2)^{2}}=\frac{1}{2} \)
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