Continuity/R/x sine 1 over x/Exercise

Show that the function

$f\colon \mathbb {R} \longrightarrow \mathbb {R}$

defined by

${}f(x)={\begin{cases}x\cdot \sin {\frac {1}{x}}{\text{ for }}x\neq 0\,,\\0{\text{ else}}\,,\end{cases}}\,$

is continuous.

Is it possible to sketch the graph of this function?

Create a solution