# Limits - HELP!

1. Nov 11, 2007

### Mattofix

1. The problem statement, all variables and given/known data

2 Questions, both find xn as n tends to infinity.

http://img229.imageshack.us/img229/5154/scan0002un5.th.jpg [Broken]

2. Relevant equations

3. The attempt at a solution

Have attempted question one but am unsure if (1/n)log(n^2) tends to 0, and if it does do i need to prove it? I dont know how to do the second q, i know that sin(expn) oscillates between -1 and 1 and exp(-n) tends to 0 as n tends to infinity

Last edited by a moderator: May 3, 2017
2. Nov 11, 2007

### HallsofIvy

Yes, (1/n) log(n^2) = (2/n)log(n) goes to 0. You might prove that by looking at 2ln(x)/x^2 and using L'Hopital's rule.

As for the second one, since sin is always between -1 and 1, you really just need to show that $\sqrt{n}/(n+ e^{-n})< \sqrt{n}/n$ (since $e^{-n}$ is always positive) converges to 0.

3. Nov 11, 2007

thanks