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Is 1(n)!\frac{1}{(n) !} A Good Bound for the Maximum Possible Error for the Error

Question 36

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Is 1(n)!\frac{1}{(n) !} a good bound for the maximum possible error for the nth degree Taylor polynomial about x = 0 approximating sin⁡(x2)\sin \left(\frac{x}{2}\right) on the interval [0, 1]?

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