Maclaurin series?

Question

Hi,

I was wondering how one would go about finding the Maclaurin series for:

f(x) = x * e^(x^2)

Maclaurin is a form of Taylor series, right? So would I just find the derivatives of the above function and plug them into the Taylor series formula?

Thanks!

Answer 1

maclaurin series(centered around x=0) of f(x+dx) is:

f(x+dx) = f(x) + (df/dx)*x + (d2f/dx2)*x^2 + (d3f/dx3)*x^3.....

so u would find the derivatives and put it in there.

the only difference between maclaurin series and taylor series is that taylor series could be centered about a value other than 0. like instead of just (df/dx)*x, its (df/dx)*(x-a) where a is the value its centered around.

Answer 2

Yes, its a particular case of Taylor, a= 0

Ana

Answer 3

yes ... maclaurin is expansion near x=0

f' = exp(x^2) + 2x^2 exp(x^2) = exp(x^2) +2xf
f'' = 2x exp(x^2) +2f +2xf' = 4f+2xf'
this will give you easier way of getting higher derivatives