Tea Time Numerical Analysis · Problem 1.2.24

Preliminaries — Leon Brin

Mathematics — Numerical Analysis · taylor-remainder

Problem

Find a bound on the error of the approximation e2≈1+2+12(2)2+16(2)3+124(2)4+1120(2)5e^2 \approx 1 + 2 + \frac{1}{2}(2)^2 + \frac{1}{6}(2)^3 + \frac{1}{24}(2)^4 + \frac{1}{120}(2)^5 according to Taylor's Theorem. Compare this bound to the actual error.

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