Need Help with Limits? Let's Tackle These Questions Together!

[Mattofix]

Limits - Please Help!

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 http://img230.imageshack.us/img230/562/scan0002ql7.th.jpg I am not asking for the answers just some help to put me on the right path.

Thanks

 

[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.

 

[Mattofix]

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

 

[Mattofix]

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