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Math Help - Maclaurin series question - am I right?

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    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:
    f(x) = xe^x + cosx

    Can I work out each part seperately and then add them?
    And is
    xe^x = x + x^2 + 3x^3/3! + 4x^4/4!...
    cosx = 1 - x^2/2 + x^4/4! - x^6/6!...

    If so then am I correct in saying the series would be:
    f(x) = 1 + x + x^2 + x^3/3 + 5x^4/4!...

    and if not, where have I screwed up?!
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    Quote Originally Posted by Dr Zoidburg View Post
    Use the definition of the Maclaurin series to find the first four non-zero terms of the Maclurin series for:
    f(x) = xe^x + cosx

    Can I work out each part seperately and then add them?
    And is
    xe^x = x + x^2 + 3x^3/3! + 4x^4/4!...
    cosx = 1 - x^2/2 + x^4/4! - x^6/6!...

    If so then am I correct in saying the series would be:
    f(x) = 1 + x + x^2 + {\color{red}x^3/3} + 5x^4/4!...

    and if not, where have I screwed up?!
    Hey, 3x^3/3!=3x^3/6=x^3/2 \neq {\color{red}x^3/3}

    But yes, you can work out each part separately
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