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Homework Help: Improper integrals

  1. Feb 16, 2005 #1
    [tex]\int_2^{inf} \frac{2}{(x+3)^{3/2}}[/tex]

    integrating the problem, i get:
    [tex]\frac{-4}{sqrt(x+3)}[/tex]

    now integrating from 2 to inf(replaced with b), plugging in 2, i get -4/5:
    f(b) + 4/5
    lim->inf

    it looks like f(b), lim->inf goes to -4 X 10^-inf

    so wouldnt the answer just be divergent? i also tried 4/5 and -4/5, but it wouldnt work. i dont really know the proper way to find the limit. all i do is plug in the largests number and try to find a pattern.
     
    Last edited: Feb 16, 2005
  2. jcsd
  3. Feb 16, 2005 #2

    Curious3141

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    What is [tex]lim_{x \rightarrow \infty}\frac{1}{x^n}[/tex] where n is any positive real number ?
     
  4. Feb 16, 2005 #3
    looks like it goes to zero
     
  5. Feb 16, 2005 #4

    dextercioby

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    Yes,that's right...

    Daniel.
     
  6. Feb 16, 2005 #5
    yes, but i still dont get it.... what are you trying to tell me?


    are you saying that f(b),lim->inf goes to zero? and the answer should be 4/5?
     
  7. Feb 16, 2005 #6

    dextercioby

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    Exactly.

    Daniel.
     
  8. Feb 16, 2005 #7
    ah, thanks for the help. actually, f(2) is not equal to 4/5, i typed it wrong in my calculator. i need some sleep, thanks agian.
     
  9. Feb 16, 2005 #8

    dextercioby

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    I realize that i didn't bother to do the calcuation for you and that's why i agreed with you...:wink:

    Daniel.
     
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