Limits -

1. Oct 27, 2007

Mattofix

I have been set 4 questions, i basically have no idea if the ones i have tried are correct and have no idea how to even start the other 2. Any help would be much appreciated. I have scanned them in (easier than typing i think).

http://img90.imageshack.us/img90/7247/scan0001dg1.th.jpg [Broken] http://img230.imageshack.us/img230/562/scan0002ql7.th.jpg [Broken]

I am not asking for the answers just some help to put me on the right path.

Thanks

Last edited by a moderator: May 3, 2017
2. Oct 27, 2007

nizi

b)use the rationalization of the numerator.
$$n \left( { \sqrt{1+n^{2}}-n } \right) = \frac{n \left( { 1+n^{2}-n^{2} } \right)}{\sqrt{1+n^{2}}+n}$$
c)watch the given hint carefully!
$$\left( { \frac{3}{2} } \right)^{2n} < \left( { \frac{2n+1}{n+1} } \right)^{2n}$$
you'd better prove the given hint by the induction...

I think the other answers are right in the way you solved.

3. Oct 27, 2007

Mattofix

thats great, youv been really helpfull, one thing though.. does that mean c) lim xn tends to infinity?

4. Oct 28, 2007

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