MathematicsMedium179×since 2002Q4296Let f,gf, gf,g and hhh be the real valued functions defined on R\mathbb{R}R as f(x)={x∣x∣,x≠01,x=0f(x)=\left\{\begin{array}{cc}\frac{x}{|x|}, & x \neq 0 \\ 1, & x=0\end{array}\right.f(x)={∣x∣x,1,x=0x=0 g(x)={sin(x+1)(x+1),x≠−11,x=−1g(x)=\left\{\begin{array}{cc}\frac{\sin (x+1)}{(x+1)}, & x \neq-1 \\ 1, & x=-1\end{array}\right.g(x)={(x+1)sin(x+1),1,x=−1x=−1 and h(x)=2[x]−f(x)h(x)=2[x]-f(x)h(x)=2[x]−f(x), where [x][x][x] is the greatest integer ≤x\leq x≤x. Then the value of limx→1g(h(x−1))\lim\limits_{x \rightarrow 1} g(h(x-1))x→1limg(h(x−1)) is :A1B−1-1−1Csin(1)\sin (1)sin(1)D0Check answerSkip