Question

lim inverse tan x as x approaches infinity

Answer 1

If x approaches \( +\infty \) then \( \tan^{-1}(x)\) approaches \( \frac \pi 2\)

Answer 2

If x approaches \( -\infty \) then \( \tan^{-1}(x)\) approaches \(- \frac \pi 2\)

Answer 3

how do you know?

Answer 4

http://www.wolframalpha.com/input/?i=plot+arctan%28x%29

Answer 5

is there anyway to deduce that?

Answer 6

What is
\[
\tan(\pi/2)
\]

Answer 7

?

Answer 8

1/0

Answer 9

And so

Answer 10

Here is another method just in case it helps.
Do you remember what the graph of tan x looks like?