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Math Help - finding a limit using a power series

  1. #1
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    finding a limit using a power series

    How would I go about finding this limit using a power series?

    finding a limit using a power series-math-pic.png

    I think I would convert this into a power series and then take the limit as x goes to zero of the resulting polynomial. However I'm not sure where to start in terms of rewriting this as a taylor series expansion.
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  2. #2
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    Re: finding a limit using a power series

    I presume you know that e^x= 1+ x+ x^2/2+ x^3/6+ \cdot\cdot\cdot= \sum \frac{x^n}{n!}.

    So e^{-3x^3}= 1+ (-3x^3)+ (-3x^3)^2/2+ (-3x^3)^3/6+ \cdot\cdot\cdot= \sum\frac{(-3x^3)^n}{n!}
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