Even though the following limit can be found using the theorem for limits of rational

functions at infinity, use L$\text{'}$H$$pital$\text{'}$s rule to find the limit$.$

$\underset{x}{lim}\frac{2x^2+3x+1}{3x^2-5x+1}$

Select the correct choice below and, if necessary, fill in the answer box to complete

your choice.

A$.\underset{x}{lim}\frac{2x^2+3x+1}{3x^2-5x+1}=$

$($Simplify your answer.$)$

B$.$ The limit does not exist.