- #1

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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!!

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- Thread starter marrie
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- #1

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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!!

- #2

tiny-tim

Science Advisor

Homework Helper

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Hi marrie! Welcome to PF!

Find c ∈ IR, like ∫∞ ( 2x - c ) dx is convergent

0 X^2 +1 2x+1

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

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?

- #3

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And I know that the bottom needs to increase than for the top for the integral converge.

thanks for your hints!!!

- #4

tiny-tim

Science Advisor

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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.

ah … but how *much* more than the top?

anyway, write the whole thing over a common denominator …

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

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