While functioning on some probability question, I had to advice $lim_x o infty arctan(x)$. I knew the prize intuitively together $pi/2$, yet i cannot number out how to prove that by elementary way (without resorting come $epsilon-delta$ arguments). How does one prove it (preferably, there is no resorting to L"Hopital"s rule)?




You are watching: Limit of inverse tangent as x approaches infinity

*

The $arctan$ role is the inverse function of $$ an:left(-fracpi2,fracpi2 ight) ightarrowBbb R$$and due to the fact that this function is monotonically boosting then$$lim_x ofracpi 2 an x=+inftyiff lim_x o+inftyarctan x=fracpi2$$


$$lim_x o +infty arctan x = fracπ2$$ and also $$lim_x o -infty arctan x = -fracπ2,$$then in total$$lim_x o infty arctan x = fracπ2 eer-selection.comrmsgn(x).$$


*

*

Thanks for contributing solution to beer-selection.comematics Stack Exchange!

Please be certain to answer the question. Administer details and also share her research!

But avoid

Asking for help, clarification, or responding to various other answers.Making statements based upon opinion; earlier them increase with recommendations or personal experience.

Use beer-selection.comJax to format equations. beer-selection.comJax reference.

To discover more, watch our advice on writing good answers.


post Your answer Discard

By clicking “Post her Answer”, friend agree to our regards to service, privacy policy and also cookie plan


Not the answer you're looking for? Browse other questions tagged borders or questioning your very own question.


Proof that the limit of the normal distribution for a standard deviation approximating 0 is the dirac delta function.
*

site design / logo © 2021 ridge Exchange Inc; user contributions licensed under cc by-sa. Rev2021.11.18.40788




See more: A Person Who Never Made A Mistake Never Tried Anything New, Albert Einstein

beer-selection.comematics ridge Exchange works ideal with JavaScript permitted
*

your privacy

By click “Accept every cookies”, girlfriend agree ridge Exchange can store cookie on your device and disclose details in accordance v our Cookie Policy.