The left-hand derivative of $f(x) = [x] \sin(\pi x)$ at $x = k$,where $k$ is an integer and $[\cdot]$ denotes the greatest integer function,is:

The left-hand derivative of $f(x) = [x]\sin(\pi x)$ at $x = k$,where $k$ is an integer and $[x]$ denotes the greatest integer function $\le x$,is:

The function $y = \sin^{-1}\left(\frac{2x}{1 + x^2}\right)$ is not differentiable for

If $f(x) = \begin{cases} \frac{1}{2}(b^2 - a^2), & 0 \leq x \leq a \\ \frac{1}{2}b^2 - \frac{x^2}{6} - \frac{a^3}{3x}, & a < x \leq b \\ \frac{1}{3}\left(\frac{b^3 - a^3}{x}\right), & x > b \end{cases}$,then which of the following is true?

Assertion $(A)$: $f(x) = |x|$ is differentiable at $x = a \neq 0$ and continuous but not differentiable at $x = 0$.
Reason $(R)$: If a function is differentiable at a point,then it is continuous at the point. But the converse is not true.

Let $f(x)=|1-2 x|$, then