What to do when l'Hopital's doesn't work I'm a first time Calc I student with a professor who loves using $e^x$ and logarithims in questions. So, loosely I know L'Hopital's rule states that when you have a limit that is indeterminate, you can differentiate the function to then solve the problem. But what do you do when no matter how much you differentiate, you just keep getting an indeterminate answer? For example, a problem like
$\lim _{x\to \infty }\frac{\left(e^x+e^{-x}\right)}{\left(e^x-e^{-x}\right)}$
When you apply L'Hopital's rule you just endlessly keep getting an indeterminate answer. With just my basic understanding of calculus, how would I go about solving a problem like that?
Thanks

why would you want to use l'hopitals on this? for $x$ large positive $e^{-x} = \frac 1{e^x}$ which is small. therefore $$\frac{e^x + e^{-x}}{e^x -e^{-x}} = \frac{e^x}{e^x}+\cdots \to 1 \text{ as } x \to \infty.$$
