Math

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Thankyou very much!
I'm having trouble with this question about taylor series.
how would i go about doing the following questoin?
thank you!


find the maclaurin series for the function
sin(x)-x+((x^3)/3!)


how do i do this?
thanks aagain

  • Math -

    A Maclaurin series expansion is a power series expansion about 0.
    Thus:
    f(x)=f(0)+f'(0)*x + f"(0)*x^2/2! + f(3)(0)x^3/3! + ....
    for sin(x),
    all the even ordered derivatives (f(0),f"(0)...) are sin(0), so the terms left are:
    sin(x)=cos(0)x-cos(0)*x^3/3!+cos(0)x^5/5!-...
    =x-x^3/3!+x^5/5!-x^7/7!+....

    So the given expression removes the first two terms of the expansion:
    sin(x)-x+((x^3)/3!)
    =x-x^3/3!+x^5/5!-x^7/7!+.... -x+x^3/3!
    =x^5/5!-x^7/7!+....

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