Find $ \lim_{n \to \infty} e^{\frac{a_n}{n}} + \sqrt{n}\sin(\frac{\sqrt{2}}{\sqrt{n}})$ Let{$ {a_n} $} be sequence of real numbers s.t $ |a_n| \le \sqrt{n} , \,\, n=1,2,3\ldots$
Find  
$$ \lim_{n \to \infty} e^{\frac{a_n}{n}} + \sqrt{n}\sin(\frac{\sqrt{2}}{\sqrt{n}})$$
My attempt got me limit of sin part in question which most probably is $\sqrt{2}$ but what to do with exponential part?

Hint  $$ \frac{a_n}{n}\leq  \frac{\sqrt{n}}{n}=   \frac{1}{\sqrt{n}}$$
