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Math Help - show funcion is solution of differential function.

  1. #1
    Senior Member
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    show funcion is solution of differential function.

    Not sure what they want here, please help.

    show funcion f(x) = n=0->infinity x^n / n!

    show that f(x) = e^x
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  2. #2
    Junior Member
    Joined
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    Australia
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    Depends what you can use. If you can just use a Taylor series this is straightforward...

    A Taylor's series is

    f(x) = \sum_{n=0}^\infty \frac{f^{(n)}(a)}{n!}(x-a)^n.

    where f^{(n)}(a) means the nth derivative of f(x) evaluated at x=a. So in your case

    f^{(n)}(x) = e^x

    and you substitute a=0 to get the result you need.

    Note: A Taylor series with a=0 is also called a Maclaurin series.

    Hope this helps.
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