Now preform something called the Cauchy Product.
On the first 5 terms in each one.
Problem- Find the terms through x^5 in the Maclaurin series for f(x)=e^(-x) * cos(x)
After trying to find f'(x), f''(x), f'''(x), and so on, the derivatives seemed overly complex. I heard that it is possible to use known Maclaurin series (e.g. e^(-x) and cos(x) separately) and then perform multiplications, divisions, etc. How would I combine them?
I'm not sure I understand the cauchy product entirely unfortunately-
I'm trying to multiply the terms from the two series- so far I have-
1+(-1)x+(1/2-1/2)x^2+[the third term]<-where I'm stuck, since there's no term in cosx with x^3. What do I multiply the x^3/3! term from e^(-x) with, if anything?
Thanks once again.