Results 1 to 3 of 3

Math Help - if B Approaches infinity, how he solved this

  1. #1
    Member moonnightingale's Avatar
    Joined
    Sep 2009
    Posts
    135

    if B Approaches infinity, how he solved this

    If B approaches to infinity, how the book solved this
    plz explain
    Attached Thumbnails Attached Thumbnails if B Approaches infinity, how he solved this-new-bitmap-image.jpg  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    A Plied Mathematician
    Joined
    Jun 2010
    From
    CT, USA
    Posts
    6,318
    Thanks
    4
    Awards
    2
    \displaystyle\lim_{B\to\infty}C=\lim_{B\to\infty}B  \,\log_{2}\left(1+\frac{S}{N_{0}B}\right)=\lim_{B\  to\infty}\frac{\ln\left(1+\frac{S}{N_{0}B}\right)}  {(1/B)\ln(2)}.

    At this point, you employ L'Hopital's Rule by taking the derivative of the top w.r.t. B, and the derivative of the bottom w.r.t. B (NOT the quotient rule):

    \displaystyle \lim_{B\to\infty}\frac{\ln\left(1+\frac{S}{N_{0}B}  \right)}{(1/B)\ln(2)}=\lim_{B\to\infty}\frac{\left(1/\left(1+\frac{S}{N_{0}B}\right)\right)\left(-\frac{S}{N_{0}B^{2}}\right)}{-(1/B^{2})\ln(2)}.

    Can you finish?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,817
    Thanks
    316
    Awards
    1
    Bah! You beat me to it, Ackbeet!

    -Dan
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Limit as X approaches infinity
    Posted in the Calculus Forum
    Replies: 4
    Last Post: September 28th 2010, 02:30 PM
  2. [SOLVED] limit as x approaches infinity w/ e
    Posted in the Calculus Forum
    Replies: 2
    Last Post: March 16th 2010, 07:07 PM
  3. Limit as x approaches infinity
    Posted in the Calculus Forum
    Replies: 1
    Last Post: January 17th 2010, 09:32 AM
  4. What is the sum as n approaches infinity?
    Posted in the Algebra Forum
    Replies: 6
    Last Post: September 7th 2009, 07:38 AM
  5. Limits As X approaches infinity
    Posted in the Calculus Forum
    Replies: 14
    Last Post: October 3rd 2008, 08:13 AM

Search Tags


/mathhelpforum @mathhelpforum