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Math Help - power series

  1. #1
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    power series

    The funtion f is defined by the power series
    f(x)= the sum n=0 to infiniti ((-1)^nx^(2n))/(2n+1)!

    Find f'(0) and f''(0) determine whether f has a local maximum, a local minimum, or neither at x=0

    Show that 1-(1/3!0 approximates f(1) with error less than 1/100

    Show that y=f(x) is a solution to the differential equation xy' + y = cosx

    any help is greatly apprectiated
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by miamirider View Post
    The funtion f is defined by the power series
    f(x)= the sum n=0 to infiniti ((-1)^nx^(2n))/(2n+1)!

    Find f'(0) and f''(0) determine whether f has a local maximum, a local minimum, or neither at x=0
    differentiate the series term by term, then set x=0 to determine f'(0),

    differentiate the series term by term twice, then set x=0 to determine f''(0),

    RonL
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