Suppose that $\underset{n}{lim}{a}_n=1,\underset{n}{lim}{b}_n=-1,$ and $n\underset{n}{lim}3a_n-4b_n$

for all $n.$ Evaluate each $of$ the following $limits,or$ state that the $limit$ does not exist, $or$ state that there $is$ not enough information $to$ determine whether the $limit$ exists.

$\underset{n}{lim}3a_n-4b_n$

$\underset{n}{lim}\sqrt[\phantom{2}]{a_n+3}$

$\underset{n}{lim}\frac{a_n+b_n}{a_n-b_n}$