(adsbygoogle = window.adsbygoogle || []).push({}); limit proof??

well what i am trying to understand,actually proof is if we can get with the limit inside a power (exponent) if the exponent is irrational.

Say we have any sequence (a_n) or any function f(x), let p be irrational then can we do the following, if yes why, if not why???

1. for the sequence

l

[tex]\lim_{\substack{\\n\rightarrow \infty}} (a_n)^{p} =(\lim_{\substack{\\n\rightarrow \infty}} a_n)^{p}[/tex] ?????

and

2.[tex]\lim_{\substack{\\x\rightarrow x_o}} (f(x))^{p} =(\lim_{\substack{\\x\rightarrow x_o}} f(x))^{p} [/tex]

I know how to prove this but only when p is from naturals. HOwever i have never come accross any such a problem. Only today suddenly this idea crossed my mind, so i thought i might get some suggesstions here.

So what is the proper answer to this??

thnx in advance

P.S if you could tell me where i could find a proof for this, i would be really grateful.

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# Limit proof?

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