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.
Chapter6: Exponential And Logarithmic Functions
Section6.2: Graphs Of Exponential Functions
Problem 52SE: Prove the conjecture made in the previous exercise.
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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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