Use induction to prove Let f(x) be a polynomial of degree n in Pn(R). Prove that...

Use induction to prove

Let f(x) be a polynomial of degree n in Pn(R). Prove that for any g(x)∈Pn(R) there exist scalars c0, c1, ...., cn such that g(x)=c0f(x)+c1f′(x)+c2f′′(x)+⋯+cnf(n)(x), where f(n)(x)denotes the nth derivative of f(x).

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Colby Messinger answered 1 year ago

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Use induction to prove Let f(x) be a polynomial of degree n in Pn(R). Prove that...

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