# Thread: show funcion is solution of differential function.

1. ## 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

2. 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.