PlanetMath: asymptote of an arctangent

(more info)

Math for the people, by the people.

donor list - find out how

Main Menu

sections Encyclopædia
Papers
Books
Expositions

meta Requests (236)
Orphanage
Unclass'd (1)
Unproven (540)
Corrections (47)
Classification

talkback Polls
Forums
Feedback
Bug Reports

downloads Snapshots
PM Book

information News
Docs
Wiki
ChangeLog
TODO List
Copyright
About

Entry average rating: No information on entry rating

asymptote of an arctangent

(Example)

Given the function $y = \tan^{-1}(x)$ ,

$\includegraphics{AsympArcTan}$

we see that it has two asymptotes, namely $\frac{\pi}{2}$ and $-(\frac{\pi}{2})$ . This specific example of an asymptote was mentioned in an episode of the comedy TV show The Big Bang Theory, in which the mathematician Sheldon Eppes tries to explain his inability to reach the top of a rock wall, getting stuck at the same height each time. According to the Mathematica manual, the results of ArcTan for real "are always in the range $- \pi / 2$ to $\pi / 2$ .