Question

Check my solution !

Answer 1

\[\huge \bf \lim_{x \rightarrow \infty}\frac{e^x~\sin(\frac{x^n}{e^x})}{x^n}\]

Answer 2

Let
\[\large \bf u=\frac{x^n}{e^x}\]
as x is approaching to infinty ,then u tends to `0`