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Math Help - How do I prove sinh x?

  1. #1
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    How do I prove sinh x?

    I need to prove the Maclarin Expansion of Sinh (x).I know Sinh (x) = (e^x - e^-x)/2 but where do go from here? Please Help.
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  2. #2
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    Sinh x

    Hello rideorsmurf
    Quote Originally Posted by rideorsmurf View Post
    I need to prove the Maclarin Expansion of Sinh (x).I know Sinh (x) = (e^x - e^-x)/2 but where do go from here? Please Help.
    Use the expansions of e^x and e^{-x}:

    e^x = 1 + x + \frac{x^2}{2!}+ \frac{x^3}{3!}+ \frac{x^4}{4!}+ \frac{x^5}{5!}+ \dots

    e^{-x} = 1 - x + \frac{x^2}{2!}- \frac{x^3}{3!}+ \frac{x^4}{4!}- \frac{x^5}{5!}+ \dots

    ... and subtract:

    e^x-e^{-x} = 2x +2\frac{x^3}{3!}+ 2\frac{x^5}{5!}+ \dots

    \Rightarrow \sinh x =x +\frac{x^3}{3!}+ \frac{x^5}{5!}+ \dots

    Grandad
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  3. #3
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    Thank you so much. That was a lot simpler than I was making it out to be.
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