Function limit/Sine 1 over x/Several factors/Exercise

Determine for the following functions, if the limit function for ${}x\in \mathbb {R} \setminus \{0\}$, ${}x\rightarrow 0$, exists, and, in case, what value it takes.

1. ${}\sin {\frac {1}{x}}$,
2. ${}x\cdot \sin {\frac {1}{x}}$,
3. ${}{\frac {1}{x}}\cdot \sin {\frac {1}{x}}$.

Create a solution