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**1) Let f(x) = (x^3) [cos(x^2)].**

a) Find P_(4n+3) (x) (the 4n + 3-rd Taylor polynomial of f(x) )

b) Find f^(n) (0) for all natural numbers n. (the n-th derivative of f evaluated at 0)

a) Find P_(4n+3) (x) (the 4n + 3-rd Taylor polynomial of f(x) )

b) Find f^(n) (0) for all natural numbers n. (the n-th derivative of f evaluated at 0)

I know the definition of Taylor polynomial but I am still unable to do this quesiton. I tried to find the first few terms but I can't see an obvious pattern. I have no problem using the definition to find the first few terms...but this is a weird question. Can someone nicely give me some hints on both parts?

Any help is greatly apprecaited!