Results 1 to 2 of 2

Math Help - Pre-Exam Calculus Questions

  1. #1
    Member
    Joined
    Dec 2009
    Posts
    171

    Pre-Exam Calculus Questions

    I will be glad to get some guidance to the following questions:

    1. Determine whether the next series converges , diverges or absolutely converges:
     \Sigma_{n=2}^{\infty} \frac{(-1)^{n}}{ln(n)} (\frac{1}{2} + \frac{2}{2^{2}} +...+\frac{n}{2^{n}} ) .

    2. Find all the values of the parameters a,b which for these values the integral converges:
     \int_{0}^{\infty} \frac{arctan(x^{2})}{\sqrt{x^{a}+x^{b}}} .

    Thanks in advance... I'll show what I've tried in the reply.
    Last edited by WannaBe; April 18th 2010 at 06:19 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Dec 2009
    Posts
    171

    ...

    About the first one:

    If we take this series from n=3 in absolute value, we can say it's less than:
     \Sigma_{n=2}^{\infty} (\frac{1}{2}+...+\frac{n}{2^{n}} )
    All I need is to show that the series above converges...The problem is that the number of conjunct elements depends on n...

    The second one:
    The only problematic point is 0 ... We can substitute  x^{2}= t or something, but I don't think it's necessary ... Because we can say it's less than  \frac{\pi}{2} \frac{1}{\sqrt{x^{a}+x^{b}}} ... I can't figure out how to use now something like the comparison test... There must be an easy way...

    About the third one- I've no idea


    Thanks a lot!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. exam problems (calculus 1)
    Posted in the Calculus Forum
    Replies: 5
    Last Post: December 15th 2010, 02:23 AM
  2. Calculus AB exam prep, dy/dt = my
    Posted in the Calculus Forum
    Replies: 2
    Last Post: January 17th 2010, 08:28 AM
  3. AP Calculus Practice Exam
    Posted in the Calculus Forum
    Replies: 2
    Last Post: August 23rd 2008, 11:44 PM
  4. Calculus Exam Problems
    Posted in the Calculus Forum
    Replies: 2
    Last Post: May 17th 2008, 08:30 PM
  5. AP Exam Questions--Help
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 25th 2008, 02:25 PM

Search Tags


/mathhelpforum @mathhelpforum