5. (a) Let f(x) and g(x) be smooth functions from R to R, show that if f(x) and g(x) have contact of order n at p then f(x) and g(x) are k-th order of approximations of one another for all k = 1,2,..., n. (b) Let f(x1,..., m) and g(x1, ..., xm) be smooth functions from Rm to R, what role does T(f), the n-th Taylor polynomial of a function f centered at the point p, play in this topic of k-th order approximation?

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A: Thanks for the question :)And your upvote will be really appreciable ;)

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A: Thanks for the question :)And your upvote will be really appreciable ;)

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