Question $4-10$ marks

Evaluate the following limits

$($a$)\underset{x}{lim}(1\frac{1}{x}{)}^x.$

$(5$ marks$)$

$($b$)\underset{x}{lim}\frac{x}{lnx}.$

$(2$ marks$)$

$($c$)\underset{x}{lim}\frac{arctan(\frac{1}{x})}{\frac{1}{x}}$

$(3$ marks$)$