Tea Time Numerical Analysis · Problem 1.2.29

Preliminaries — Leon Brin

Mathematics — Numerical Analysis · maclaurin-series

Problem

Suppose you wish to approximate the value of −e4sin⁡4-e^4 \sin 4 using separate Maclaurin polynomials (Taylor polynomials expanded about x0=0x_0 = 0) for the sine and exponential functions instead of a single Maclaurin polynomial for the function f(x)=−exsin⁡xf(x) = -e^x \sin x. How many terms of each would you need in order to get accuracy within 10−2010^{-20}? Ignore round-off error.

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