$\displaystyle
\displaystyle\lim_{x\to\infty}
$
(1-1/x)^5x
Can someone please help with this one i dont even know where to start?
thank you
Hello, cowboys111!
I believe you are expected to know that: .$\displaystyle \lim_{u\to\infty}\left(1 + \frac{a}{u}\right)^u \;=\;e^a$
$\displaystyle \displaystyle\lim_{x\to\infty}\left(1-\frac{1}{x}\right)^{5x}$
We have: .$\displaystyle \lim_{x\to\infty}\left[\left(1 + \frac{\text{-}1}{x}\right)^x\right]^5 \;=\;\left[\lim_{x\to\infty}\left(1 + \frac{\text{-}1}{x}\right)^x\right]^5\;=\;\left[e^{-x}\right]^5 \;=\;e^{-5x}
$