Show that the function `f(x)={xsin1/x\ \ \ ,\ \ \ \ w h e n\ x!=0 0\ \ \ \ \ \ \ \ \ \ \ w h e n\ x=0` is continuous but not differentiable at `x=0` .

Explanation

To show that the function

\[
f(x) =
\begin{cases}
x \sin\left(\frac{1}{x}\right) & \text{when } x \neq 0 \\
0 & \text{when } x = 0
\end{cases}
...