# Limits as n approaches infinity

lim n-> infinity of:

(n^4 + n^2 + 1)^0.5 - n^2 -1

sin(2/n)/(1/n)

(ln(n) + e^n)/(2^n + n^2)

If anyone could explain the processes required to obtain the limits of any.. (or all) of these statements, that would be great

In the first one, you could multiply the expression by its conjugate.

For the second one, recall the identity lim t->0 sin(t) /t = 1. (substitute 2/n = t as t->0)

For the third one, just apply l'hopital's rule several times.

HallsofIvy