# Thread: limits indeterminate form

1. ## limits indeterminate form

$
\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

2. Hello, cowboys111!

I believe you are expected to know that: . $\lim_{u\to\infty}\left(1 + \frac{a}{u}\right)^u \;=\;e^a$

$\displaystyle\lim_{x\to\infty}\left(1-\frac{1}{x}\right)^{5x}$

We have: . $\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}
$

3. I sure that it is a typo.
The limit is $e^{-5}$.

4. ok thats easy enough i just didnt know that
thanks for the help