Expert: Sherman D. - 6/12/2004

Question
hi if possible please help, thank u

Make equation for f(x)= e ^ (x^3) using the Taylor series


Example: f(x)= e^(-x) = sum (-1)^n(x)^n/ n!

Answer
according to http://www.efunda.com/math/taylor_series/exponential.cfm

e^x = 1 + (x/(1!)) + ((x^2)/(2!)) + ((x^3)/(3!)) + ....
or the way i like to right it

or you can say

e^x = 1 + x + ((x^2)/(2!)) + ((x^3)/(3!)) + ....

and

e^(-x^2) = 1 - (x^2) + ((x^4)/(2!)) - ((x^6)/(3!)) + ((x^8)/(4!)) - ....

so i believe this one mean that

e^(-x) = 1 + x - ((x^2)/(2!)) + ((x^3)/(3!)) - .... I think, but since it doesn't have it on the website, i am just going to take the e^(-x^2) as how to do it.

so i believe the answer is

e^(x^3) = 1 + x^3 + ((x^6)/(2!)) + ((x^9)/(3!)) + ((x^12)/(4!)) + ....

But i am not completely certain since i have never done Taylor Series, i am just working with what i see not what i know.