[MOVED] Understanding Graph and Asymptote question.

[oshea.emma]

Hi everyone... I have figured out some of this question... I just need help on 1 part.

OK so the question is:

I have completed parts 1 and 2 myself... And I know the answer to part 3 but I just don't understand how to calculate it or understand it. Any help is much much appreciated! Thanks

So here's what I've got so far.

And here's the graph plotted..

How do I calculate the asymptote to be PI over 2? Any thoughts?

 

[galactus]

Try the limit of arctan as x appraoches infinity.

\(\displaystyle \L\\\lim_{x\to\infty}\text{tan^{-1}(x)}\)

\(\displaystyle \L\\\lim_{x\to{-}\infty}\text{tan^{-1}(x)}\)

What does arctan approach as x approaches infinity. Try larger and larger values. I believe you know the answer.

 

[oshea.emma]

Yes...It is undefined and the corresponding calculation is PI over 2.
Thank you very much!

 

[galactus]

It is undefined at pi/2, but the limit approaches pi/2 as x approaches infinity.