Originally Posted by

**Dr Zoidburg** Use the definition of the Maclaurin series to find the first four non-zero terms of the Maclurin series for:

$\displaystyle f(x) = xe^x + cosx$

Can I work out each part seperately and then add them?

And is

$\displaystyle xe^x = x + x^2 + 3x^3/3! + 4x^4/4!...$

$\displaystyle cosx = 1 - x^2/2 + x^4/4! - x^6/6!...$

If so then am I correct in saying the series would be:

$\displaystyle f(x) = 1 + x + x^2 + {\color{red}x^3/3} + 5x^4/4!...$

and if not, where have I screwed up?!