Real numbers/Null sequences/Behavior of inverse sequences/Exercise

Give examples of convergent sequences of real numbers ${}{\left(x_{n}\right)}_{n\in \mathbb {N} }$ and ${}{\left(y_{n}\right)}_{n\in \mathbb {N} }$ with ${}x_{n}\neq 0$, ${}n\in \mathbb {N}$, and with ${}\lim _{n\rightarrow \infty }x_{n}=0$ such that the sequence

${\left({\frac {y_{n}}{x_{n}}}\right)}_{n\in \mathbb {N} }$

1. converges to ${}0$,
2. converges to ${}1$,
3. diverges.

Create a solution