We must use the taylor remainder method by taylors

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the upper error bound method”. We must use the Taylor remainder method. - By Taylor's remainder theorem the error would be - The maximum value of e c for c in [0, 1] is e 1 which is less than 3. - So we want n such that - Using a calculator we see that if n = 6, So approximates e with an error R 6 (1) < 0.0005952 < 0.001. 31.3.2 Example Using a spreadsheet or a calculator to approximate the value of e 0.1 with the 5 th degree Taylor polynomial of e x centered at 0 and give an upper bound for the error. (Assume that it is known that e is some value between 2 and 3.) Solution: We first compute T 5 (0.1): We compute an upper bound for the error: So the using T 5 (0.1) as an approximation of e 0.1 gives an error < 0.000000002