1-e^(-x)=5e^(-2x)+3x^(-x)

Printable View

- Jul 17th 2011, 12:54 PMJamesBond16problems with Euler's number..
1-e^(-x)=5e^(-2x)+3x^(-x)

- Jul 17th 2011, 12:58 PMe^(i*pi)Re: problems with Euler's number..
I don't think there is an analytical way to solve because of the $\displaystyle x^{-x}$ term. Should that read $\displaystyle e^{-x}$ per chance?

- Jul 17th 2011, 01:03 PMJamesBond16Re: problems with Euler's number..
3x^(-x) is correct

- Jul 17th 2011, 02:57 PMAlso sprach ZarathustraRe: problems with Euler's number..
If$\displaystyle f(x)=1-e^{-x}-5e^{-2x}-3x^{-x}$

Then, $\displaystyle f(1)<0$ and $\displaystyle f(3)>0$, so there is at least one root in $\displaystyle [1,3]$.