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Find c likes the series is convergent

  • Thread starter marrie
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  • #1
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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!!
 

Answers and Replies

  • #2
tiny-tim
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Welcome to PF!

Hi marrie! Welcome to PF! :smile:
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:
 
  • #3
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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!!!
 
  • #4
tiny-tim
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Homework Helper
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Hi marrie! :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.
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:
 

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