Question: How to show that the limit as x goes to infinity of a given polynomial diverge? We have(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \lim_{x \rightarrow \infty} a_nx^n + a_{n-1}x^{n-1}+...+a_1x+a_0[/tex]

but cannot say the this limit is the sum of the limit of each term separetly because none of these limit exist. We cannot do this either

[tex] \lim_{x \rightarrow \infty} a_nx^n + a_{n-1}x^{n-1}+...+a_1x+a_0 = \lim_{x \rightarrow \infty} x^n(a_n + \frac{a_{n-1}}{x}+...+\frac{a_1}{x^{n-1}}+\frac{a_0}{x^n}) [/tex]

and say the the limit is the product of the limit because one of the limit does not exist. So what then?

Thank you.

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# Homework Help: Limit of a polynomial

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