Find the $n$-th order Taylor Polynomials for $f(x)=\sin x$ centered at $0$ and at $\frac{pi}{6}$; call these $T_{0,n}(x)$ and $T_{\pi/6,n}$, respectively. Then show that the sequence $(T_{0,n}(x))$ converges uniformly to $f(x)$ on any interval $[-M, M]$.
Taylor Polynomials
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real-analysis
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1What did you try and where are you stuck? – 2012-12-09
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0@Dirk To be honest I'm stuck at the beginning. I know what the general Taylor Polynomial looks like, but what is the difference between that and the n-th order. – 2012-12-09