Thread: Maclaurin series question - am I right?

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:
$\displaystyle f(x) = 1 + x + x^2 + x^3/3 + 5x^4/4!...$

and if not, where have I screwed up?!

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?!

Hey, $\displaystyle 3x^3/3!=3x^3/6=x^3/2 \neq {\color{red}x^3/3}$

But yes, you can work out each part separately