Saturday, 15 December 2012

limits - Proving limxtoinfty(x2+1)(fracpi2arctanx) doesn't exist.

How can I show that lim doesn't exist? I used the fact that \arctan{x}\ge x-\frac{x^3} {3}, so the initial limit is less than \lim_{x\to\infty} \frac{x^5}{3} +O(x^4), therefore the limit tends to infinity.



Is this enough? If not, then how can I show this rigorously?

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