Find c likes the series is convergent

  • Thread starter Thread starter marrie
  • Start date Start date
  • Tags Tags
    Convergent Series
Click For Summary

Homework Help Overview

The problem involves determining a value for c such that the integral from 0 to infinity of the expression (2x/(x^2 + 1) - c/(2x + 1)) is convergent. The context is within the realm of calculus, specifically focusing on improper integrals and convergence criteria.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the possibility of integrating the components of the expression separately and question whether each part converges or diverges. There is also consideration of how the growth rates of the numerator and denominator affect convergence.

Discussion Status

The discussion is ongoing, with participants offering hints and exploring the implications of their reasoning. There is acknowledgment of the need to analyze the components of the integral separately and to consider how to adjust c to influence convergence.

Contextual Notes

Participants are working under the constraints of homework guidelines, which may limit the extent of direct assistance provided. There is an emphasis on understanding the behavior of the integral rather than arriving at a definitive solution.

marrie
Messages
2
Reaction score
0
Find c ∈ IR, like ∫∞ ( 2x - c ) dx is convergent
0 X^2 +1 2x+1

I need your help because I was trying to resolve the problem, but I couldn't, is difficult for me.
Please help me!
 
Physics news on Phys.org
Welcome to PF!

Hi marrie! Welcome to PF! :smile:
marrie said:
Find c ∈ IR, like ∫∞ ( 2x - c ) dx is convergent
0 X^2 +1 2x+1

hmm :rolleyes: … you mean [tex]\int_0^{\infty}\left(\frac{2x}{x^2+1} - \frac{c}{2x+1}\right)dx[/tex] :wink:

Hint:

i] can you integrate each of them separately? does each converge or diverge?

ii] how much faster do you think the bottom needs to increase than the top for the integral to converge? :smile:
 
Ok, if I integrate each of them separately, I believe that the series diverge.
And I know that the bottom needs to increase than for the top for the integral converge.
thanks for your hints!
 
Hi marrie! :smile:
marrie said:
Ok, if I integrate each of them separately, I believe that the series diverge.
And I know that the bottom needs to increase than for the top for the integral converge.

ah … but how much more than the top? :wink:​

anyway, write the whole thing over a common denominator …

then what does c have to be to make the top increase slowly enough? :smile:
 

Similar threads

Does this series converge uniformly?
  • · Replies 7 ·
Replies
7
Views
2K
Proving convergence and divergence of series
  • · Replies 3 ·
Replies
3
Views
2K
For what values of ##\beta## does the series converge?
  • · Replies 2 ·
Replies
2
Views
2K
Series investigation: divergence/convergence
  • · Replies 8 ·
Replies
8
Views
2K
On the ratio test for power series
  • · Replies 2 ·
Replies
2
Views
2K
Proving convergence of rational sequence
  • · Replies 2 ·
Replies
2
Views
2K
Studying the convergence of a series with an arctangent of a partial sum
  • · Replies 7 ·
Replies
7
Views
2K
A problem with the convergence of a series
  • · Replies 5 ·
Replies
5
Views
2K
Maclaurin Series When 0 is in the Denominator?
  • · Replies 48 ·
2
Replies
48
Views
7K
Root test proof using Law of Algebra
  • · Replies 6 ·
Replies
6
Views
2K