A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 5 years ago

determine if the integral 1 / (1+x^2)^1/2 converges or diverges (Hint. use comparison test) so far i compared it to integral 1/ (x^2)^1/2 but that diverges

  • This Question is Closed
  1. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    cantor u there

  2. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    It diverges. I used the p series test though. If you distribute the exponent of 1/2, you get x^1/2, and 1/2 < 1 so it is divergent. If you are required to use the ratio test, you must use a function that gives values smaller than the original.

  3. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I'm sorry not x^1/2 but it equals 1/x which if you use the integral test goes to the natural log, which is divergent. Also according to the p series test, the degree in the denominator must not equal one, so either way it diverges.

  4. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    If you need to use the comparison test, you'd compare it to 1/x because in the example you used, you must distribute the exponent.

  5. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    but its the wrong comparison

  6. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    how do you compare it

  7. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i am using the comparison test, so 0< integral g(x) < integral f(x)

  8. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    if integral g(x) diverges, then integral f(x) diverges , find integral g(x)

  9. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Yes, the function you choose must be smaller. In this instance, the +1 doesn't matter, giving us 1/(x^2)^1/2, so if you distribute the one half, you get 1/x, which we can is the function g(x). We know g(x) diverges because of the several tests I mentioned above (both the integral, ratio, and p series tests) which means that the function f(x) which is 1/(1+x^2)^1/2, riveted as well. Therefore, because g(x) diverges, so does f(x). Does that answer your question?

  10. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    no because 1/x^2 ^1/2 is greater than 1 / ( 1 + x^2 ) ^1/2

  11. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    its in the wrong order

  12. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    In this instance it doesn't matter, because if you take the limit as you approach infinity, the +1 doesn't matter. It's like 1/10000000 is hardly different from 1/10000001.

  13. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    but youre not using the comparison test then

  14. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    but i see your point

  15. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    oh, hmmmm, dunno

  16. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    You can check it by the Alternating series test. If it still diverges, it absolutely diverges.

  17. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    its not an alternating series though

  18. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    If there was an x! Or another variable, then it would change things, but a constant is irrelevant in this instance.

  19. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yo cantor

  20. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I know it's not alternating. You use the alternating test to check for absolute divergence or convergence. For example, 1/x is conditionally divergent because if it alternates, it converges. If there is no alternating piece, it diverges. Hence, you can use the alternating test to check if it always diverges or only sometimes.

  21. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    hmmm, how is that relevant

  22. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    It allows you to check convergence or divergence. That was your question originally.

  23. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    cantor

  24. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ???????

  25. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yeah, this question im getting tutored for im sorry

  26. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i promise i will answer your question

  27. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I'm saying, if you have a choice, I wouldn't use the comparison test. If you don't, then just do the same thing with the denominator that is larger and use one of the methods I discussed earlier to see.

  28. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    can yuo give me a formal method

  29. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    You mean show you the steps? To which one? The comparison test? The p series? The integral test?

  30. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    any , the comparison test fails, as i explained earlier

  31. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    the direct integral comparison test

  32. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    cantor can u help me now, I have 2 parts left and I'm done. first question at the top

  33. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    one sec

  34. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.