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The function is $f(x) = 2\cos x. $ Again, $a = \pi/2$ and $n \to\infty$.

I was to do this for $n = 3$ as well and I had no problems doing that at all, but I'm confused on how you do it for for $n \to\infty$. Any tips for getting started on that?

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    What are $a$ and $n$ in your question?2011-06-23

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Hint: For any $x \in \mathbb{R}$ fixed, and as $n \to \infty$, $ |R_n (x)| \le \frac{{2|x - a|^{n + 1} }}{{(n + 1)!}} \to 0. $