Question

How do you find the limit of `arctan(x)` as x approaches infinity?

Answer 1

The limit is `pi/2` against the principal-value convention for `y = arc tan x.`
General limit `(2n+1/2)pi, n= 0, +-1, +-2, +-3, ...`,

Explanation:

For the principal value `y = arc tan x`, as `x to oo, y to pi/2`

The general limit

= the principal-value limit `+ npi, n = 0, +-1, +-2, +- 3, ...`.

So, the general limit is `pi/2+`even multiple of pi`, as` x to oo#

and `pi/2+`odd multiple of `pi`, as x `to -oo`.