This is what I'd do:
for some value of
Likewise for some K and:
Hey guys,
I'm having a REAL problem with the following limit
I've tried the squeeze rule, but an upper bound eludes me. I've only found the lower bound, which is just 0. I've tried to group together all of the powers of p, as follows:
and maybe use the fact that
tends to zero as p tends to infinity, since the bottom half rises faster than the top half. However, I'm stuck because I don't know how to go about this formally, or if this is the right way to go about it. I'd be really grateful if help was provided, and possibly a solution.
Thank you very very much in advance.
HTale
Hey Shawsend, thanks a billion for your quick reply. But I have one question regarding this part:
for some value of
Can I assume that the polynomial is an integer if it is given for some fixed x? I think also the question applies for the other part too. That is, when writing the solution out, should I state that this is for a fixed x?
Thanks in advance
HTale
EDIT: Also, how would I go about proving the final limit? Just a few pointers will do. Once again, thanks in advance!
I treated it as for a fixed and fixed set of , I could always find a C which would make the expression true and as far as pointers, I'm sorry, I don't feel I'm good enough in analysis to be giving pointers. I just stated what I'd do. Maybe the analysis experts in here can make it more rigorous.
This is very easy indeed...assuming I am understanding it correctly...by that I mean I am assuming that
If so then similarly to the previous answer let
[tex]\Therefore
Now using the fact that
We can rewrite this as
From there it should be pretty apparent the answer is zero