How do you find horizontal asymptotes for f(x) = arctan(x) ?

[ad_1]

By limitation, ##arctan x## is the inverse discharge of the neutralization of the tangent discharge ##tan## to the meantime ##(-pi/2,pi/2)## (see ).

The tangent discharge has perpendicular asymptotes ##x=-pi/2## and ##x=pi/2##, for ##tan x=sin x/cos x## and ##cos pm pi/2=0##.

Moreover, the graph of the inverse discharge ##f^(-1)## of a one-to-one discharge ##f## is obtained from the graph of ##f## by meditation environing the method ##y=x## (see ), which transforms perpendicular methods into dull methods.

Thus, the perpendicular asymptotes ##x=pm pi/2## for ##y=tan x## fit in this meditation to the dull asymptotes ##y=pm pi/2## for ##y=arctan x##.

Here's a graph of arctan(x):

Show past

[ad_2]
Source integrate