Under the same hypotheses as exercise 11, show that the Taylor expansion of f.g at 2o is obtained by taking Tn(f, xo, x)T,(g, xo, r) and retaining only the powers of (x – xo) up ton.
Under the same hypotheses as exercise 11, show that the Taylor expansion of f.g at 2o is obtained by taking Tn(f, xo, x)T,(g, xo, r) and retaining only the powers of (x – xo) up ton.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.2: Norms And Distance Functions
Problem 41EQ
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Could we answer #12?
Transcribed Image Text:11. Suppose f and g are C" functions with Taylor expansions denoted
Ta(f, xo, x) and Tn(g, xo, x). Prove that T,(f, xo, x)+ T,(9, x0, x)
is the Taylor expansion of f +g at to.
12. Under the same hypotheses as exercise 11, show that the Taylor
expansion of f.g at 1o is obtained by taking T,(f, ¤o, x)T, (9, xo, x)
and retaining only the powers of (x – ro) up to n.
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