how to evaluate a limit similar to Euler identity? I have a limit as $x$ approaches infinity of $(1+4/(7x))^x$. Solutions I saw included transforming it into $e$ to the power of natural $\log$ etc. but I've seen a way simpler transformation but can't remember it. Any help appreciated.

In general for every real $a$, $\lim_{x\to \infty}(1+a/x)^x=e^a$. Indeed, it is the same as $(\lim_{y\to\infty}(1+1/y)^y)^a=e^a$ (replace $x/a$ by $y$). So the answer is $e^{4/7}$.
