Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Bernoulli's Rule

  1. Apr 7, 2013 #1
    In his treatment of L'hôpital/Bernoulli's rule (please see attached), Rudin before ineq. ## (17)## mentions that since the differentiable quotient

    ##\frac{f'(x)}{g'(x)} \rightarrow A## as ##x \rightarrow a## and ##A<r## then there exists a pt ##c \in (a,b) \ s.t. \ a<x<c \Rightarrow \ \frac{f'(x)}{g'(x)}<r##

    Is it so because ##x## approaches ##a## that's why he used ##a<x<c## instead of ##c<x<b##

    and why this ##c## in the first place? What's wrong with just saying, ##\exists x \in (a,b)## etc
     

    Attached Files:

    Last edited: Apr 7, 2013
  2. jcsd
  3. Apr 8, 2013 #2

    mathman

    User Avatar
    Science Advisor
    Gold Member

    The theorem is not there exists an x in the interval, but rather for all x, a < x <c, f'/g' < r.
     
  4. Apr 21, 2013 #3
    True. Thanks
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook