Can someone please help?
I need to use L Hopital's Rule to find the limit: $$ \lim_\limits{x\to e}\frac{x-e}{\frac xe-1} $$
I know I need to find the derivative of the top and bottom, but since the derivative of $e$ is $e$, I can't seem to figure out what to do next.
Thank you!
The derivative of $x-e$ is $1$, because $e$ is a constant. The derivative of $\frac xe-1$ is $\frac1e$ since $\frac1e$ is the coefficient of $x$. Thus after taking derivatives the ratio becomes $1/\frac1e$ which equals $e$.