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Math Help - Taylor Polynomial & Remainder

  1. #1
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    Taylor Polynomial & Remainder

    given f(x) = x/(1-x)

    a) determine the Taylor polynomial of order 3 to f expanded about x=0

    b) write an equation for the remainder term of order 3, R3(x), in the taylor series for f

    I don't know how to solve this problem.

    any help is greately appreciated

    thanks
    k
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  2. #2
    o_O
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    T_{3}(x) = f(0) + f'(0)x +\frac{f''(0)}{2!}x^{2} + \frac{f'''(0)}{3!}x^{3}

    So all you really need is to find f'(0), f''(0), and f'''(0).

    ------------------------------------------

    R_{3}(x) = \underbrace{\frac{f^{(n+1)}(c)}{(n+1)!}x^{n+1}}_{n  =3} = \frac{f^{(4)}(c)}{4!}x^{4} \quad c \in (x_{0} = 0, x)

    Find the 4th derivative of f(x) and you should be set.
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