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Limits: How to evaluate $\lim_{x\rightarrow \infty}\sqrt[n]{x^{n}+a_{n-1}x^{n-1}+\cdots+a_{0}}-x$

Anybody can help me with this limit? I appreciate any idea. Thanks for providing the information on this great site: D $$\lim_{x \to \infty } \sqrt[n]{f(x)} - \sqrt[m]{g(x)}$$ where $$f(x)=a_0+a_1x+a_2x^2+\cdots+a_{n-1}x^{n-1}+x^n$$ and $$g(x)=b_0+b_1x+b_2x^2+\cdots+b_{m-1}x^{m-1}+x^m$$

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mathsalomon
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    The question, once expanded, could be quite similar to http://math.stackexchange.com/questions/30040 – Did Jul 24 '11 at 05:53
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    Funny: the prediction in my last comment is now confirmed. Thus the present question is a duplicate. – Did Jul 24 '11 at 07:09
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    Rewriting the limit as $\lim(f(x)^{1/n}-x)-\lim(g(x)^{1/m}-x)$ - since both limits exist their difference must equal the original limit - and then using the work of the earlier question linked above we know that the answer is $a_{n-1}/n-b_{m-1}/m$. – anon Jul 24 '11 at 07:44

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