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Math Help - maclaurin series quick Q

  1. #1
    Member i_zz_y_ill's Avatar
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    maclaurin series quick Q

    with the maclaurin series is the expansion or answer wateva to arsinh(4/3+x)

    = f(0)+(f'(0))/2! x (x)^2 + (f''(0))/3! x (x)^3....

    or is it f(0)+(f'(0))/2! x (4/3+x)^2 + (f''(0))/3! x (4/3+x)^3.....???
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  2. #2
    o_O
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    The latter. The Maclaurin series is given as:

    f(x) = 1 + f'(0)x + \frac{f''(0)}{2!}x^{2} + \frac{f^{(3)}(0)}{3!}x^{3} + ...

    Here, you are dealing with f\left(\frac{4}{3} + x\right) with f(x) = sinh^{-1} x
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