How to prove the definition of arctangent function using integral?

Join the discussion
Ask a follow-up here, or get your own question answered by working scientists, mathematicians and engineers — people, not an autocomplete.
Real named experts · corrections over time · the nuance an AI answer skips
Sign up Log in
1 reply · 2K views
zhongbeyond
Messages
3
Reaction score
0

Homework Statement


This is a problem from Introduction to Analysis by Arthur P. Mattuck,chapter 20,problem 20-1.

<a href="http://www.flickr.com/photos/86024731@N04/8090259684/" title="arctangent by gnu is not unix, on Flickr"><img src="http://farm9.staticflickr.com/8193/8090259684_a5ce06801e.jpg" width="500" height="325" alt="arctangent"></a>

I have worked out question (a),(b),(c),but I am stucked in question (d).
Please help,thanks.
 
Last edited by a moderator:
Physics news on Phys.org
For d.) you will need to compare the given integral to the integral of some other function which you can show (easily) has limiting value < or = to 2.5 at infinity.
Suggestion: consider changing the numerator to make it integrable. Be sure to check that your comparison function is everywhere bigger. (You may need to use some glue.)