Would I be right in thinking that: $x^ab^x\to0$ as $x\to \infty\,\,\forall a\in \mathbb R$ where $b\in [0,1)$? I think that $b^x$decays faster than the growth of $x^a$ but how might I prove that?
Order of convergence
2
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real-analysis
analysis
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3Yes, but how to prove it? Do you know some result that might help? Have you already done some case (like $xe^{-x}$) so that you can examine the proof and see what may apply in this case? In summary, SHOW YOUR ATTEMPT, don't expect us to do it for you. – 2011-09-18
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0@GEdgar In fairness, the OP has explained what he thinks will happen and why he thinks that will be the case. It's not like it's a verbatim copy of a homework question. – 2013-03-06