Thread: finding a limit using a power series

1. finding a limit using a power series

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

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.

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