1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Calculation of limit. L'Hopital's rule

  1. Jun 3, 2017 #1
    Problem: Evaluate lim(x->0) x cotx

    My attempt:
    lim(x->0) x cotx = lim(x->0) x cosx / sinx = lim(x->0) cosx * lim(x->0) x / sinx = 1 * lim(x->0) x / sinx = lim(x->0) x / sinx

    P.S.
    I know I must/can use L'Hopital's rule to evaluate indeterminate limits, but no matter how many times I derive x/sinx I will always have sinx (in some power) in denominator.

    I also tried different grouping of variables but still same scenario.

    maybe I don't see something so even little hint would be nice...
     
  2. jcsd
  3. Jun 3, 2017 #2

    Mark44

    Staff: Mentor

    ##\lim_{x \to 0} \frac{\sin(x)}x## is a well-known limit that should be shown in your calculus textbook. It's also a limit that can be obtained using L'Hopital.
    L'Hopital's Rule doesn't apply to all indeterminate limits, just those of the forms ##[\frac 0 0]## or ##[\pm \frac \infty \infty]##. Even then, it sometimes doesn't work, as it just gets you back to the same limit you started with.
    BTW, in future posts, please don't delete the Homework Template.
     
    Last edited: Jun 3, 2017
  4. Jun 3, 2017 #3
    L'Hopital's rule says ##\lim_{x -> a} \frac{f(x)}{g(x)} = \lim_{x -> a} \frac{f'(x)}{g'(x)}## if both ##f(x)## and ##g(x)## tend either to ##0## or ##\infty## as ##x -> a##. Maybe you're using the quotient rule for derivatives which is wrong, because that's not what the rule says.
     
  5. Jun 3, 2017 #4
    dgambh thank you very much. I was stuck on this for days and now I know why :D thank you very much again!!!

    Mark44 thank you for too.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Calculation of limit. L'Hopital's rule
Loading...