Tea Time Numerical Analysis · Problem 1.2.2

Preliminaries — Leon Brin

Mathematics — Numerical Analysis · taylor-polynomials

Problem

Let f(x)=4x3−2x2+8x−9f(x) = 4x^3 - 2x^2 + 8x - 9. ((a)) Find T3(x)T_3(x) and R3(x)R_3(x) expanded about x0=0x_0 = 0. ((b)) Find T3(x)T_3(x) and R3(x)R_3(x) expanded about x0=2x_0 = 2. ((c)) Make a conjecture based on your answers to parts (a) and (b). Can you prove it?

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