Answer
$\lim\limits_{n \to \infty} tan^{-1} n = \frac{\pi}{2}$
Work Step by Step
To find the limit, we can keep increasing $n$ and see if the function approaches a certain value.
$tan^{-1} (0) = 0$
$tan^{-1} (10) =1.471$
$tan^{-1} (100) = 1.561$
$tan^{-1} (1000) = 1.570$
$tan^{-1} (10000) = 1.571$
$tan^{-1} (100000) = 1.571$
Since $tan^{-1} n$ seems to approach $\frac{\pi}{2}$ as $n$ increases, the limit is $\frac{\pi}{2}$.
