#### Answer

$\lim\limits_{n \to \infty}$ (3+5n^2)/(n+n^2)
$ \lim\limits_{n \to \infty}$ n^2((3/n^2)+5)/n^2((1/n)+1)
= (0+5)/(0+1)
=5
sequence converges on 5

#### Work Step by Step

take limit of sequence as n approaches infinity
pull out n^2 from both the denominator and numerator
cancel out n^2
$ \lim\limits_{n \to \infty}$ (3/n^2) equals 0 because numerator is so small compared to denominator
$ \lim\limits_{n \to \infty}$ (1/n) also equals 0 because numerator is so small compared to denominator
plug in numbers and solve