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

1 Answer
A. S. Adikesavan
Jul 4, 2016

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#.

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