ECON 11A Study Guide - Midterm Guide: Decimal Mark
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Review questions 6 ams 11a: the degree 10 taylor polynomial for f (x) = ex centered at x0 = 0 is given by. T10(x) = f (0) + f(cid:48)(0)(x 0) + x4. 720 since for all k, and e0 = 1. f (k)(x) = dk dxk (ex) = ex f (10)(0) Comment: if we use t10(1) to approximate the value of e = e1, then we obtain the estimate e 1 + 1 + The rst 7 digits after the decimal point are correct: if g(x) = 3 x = x1/3, then g(cid:48)(x) = x 2/3/3 and g(cid:48)(cid:48)(x) = 2x 5/3/9. Evaluating g(x) and its rst two derivatives at x = 1000, we nd that g(1000) = 10, g(cid:48)(1000) = The second degree taylor polynomial for g(x) = 3 x, centered at x = 1000 is therefore equal to. = 10. 003332222 . (the decimal expansion has nothing but 2"s from the seventh point on).
