If f(x)=sin−1⁡([x]+x)[x],[x]≠0 =0,[x]=0where [x] denotes the greatest integer less than or equal to x, then limx→0 f(x) is

If $\begin{array}{l} f (x) = \frac{\sin^{- 1} ([x] + x)}{[x]}, [x] \neq 0 \\ = 0, [x] = 0 \end{array}$
where $[x]$ denotes the greatest integer less than or
equal to $x$ , then $lim_{x \to 0} f (x)$ is

$\begin{array}{l} lim_{x \to 0 -} f (x) = lim_{x \to 0 -} \frac{\sin^{- 1} (x - 1)}{- 1} = \frac{π}{2} \\ lim_{x \to 0 +} f (x) = 0 \end{array}$

Related content