Limits as n approaches infinity

[noland0]

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

 

[zcd]

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]

Since this is your homework, try before you ask for help and then show what you have tried.