find power series representation f(x)=xln(4-x)?

calculus 2 homework help

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  • 1 decade ago
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    you should start with the power series representation of ln(1+x), because this is one of the standard ones that is either given or you have memorized

    ln(1+x) = x - (1/2)x^2 + (1/3)x^3 - (1/4)x^4 + . . .

    so ln(4-x) is what you get when you sub in 3-x in for x in the above equation

    ln(4-x) = (3-x) - (1/2)(3-x)^2 + (1/3)(3-x)^3 - (1/4)(3-x)^4 + . . .

    and now, xln(4-x) is when you multiply the entire series above by x

    xln(4-x) = x(3-x) - x(1/2)(3-x)^2 + x(1/3)(3-x)^3 - x(1/4)(3-x)^4 + . . .

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  • Anonymous
    1 decade ago

    y=x*ln(4-x), z=ln(4-x), z’=-1/(4-x), z’’=-1/(4-x)^2, z’’’=-2/(4-x)^3 ,,,, z(jth’)=(j-1)!/(4-x)^j

    Tailor S=x*{ln(4) – x/4 – x^2/(2*4^2) – x^3/(3*4^3) – x^4/(4*4^4) +++ };

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