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!

Function with denominator zero

  1. Jul 27, 2009 #1
    1. The problem statement, all variables and given/known data

    This is a limit problem but what I need to figure out is simpler so I thought I'd post it under pre-calc. The question is:

    Find the limit:

    lim as x approaches 0 of (tan 2x)/x

    2. Relevant equations



    3. The attempt at a solution

    Since x is in the denominator I know that I must re-write (tan 2x)/x so that the denominator doesn't equal zero. I also know that 0 is a root of both the numerator and denominator, but I don't know how to re-write such an equation. Any help? Thanks!
     
  2. jcsd
  3. Jul 27, 2009 #2
    Use L'Hopital's Rule
     
  4. Jul 27, 2009 #3

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    If you haven't done l'Hopital yet, do you know lim x->0 tan(x)/x=1 or lim x->0 sin(x)/x=1? Then you could just do the variable substitution u=2x.
     
  5. Jul 28, 2009 #4
    Why can't we obtain the limit here by squeezing?

    I'll show you a similar example with tan(x) instead of (tan 2x):

    [tex]\lim_{x \to 0} \frac{tanx}{x} = \lim_{x \to 0} (\frac{sin x}{x}.\frac{1}{cos x})[/tex]

    [tex](\lim_{x \to 0} \frac{sin x}{x})(\lim_{x \to 0} \frac{1}{cos x}) = (1)(1) =1[/tex]

    In your question you must do some manipulation for the 2 in tan2x.
     
  6. Jul 28, 2009 #5

    Mark44

    Staff: Mentor

    You're not actually doing any "squeezing" here--just using the fact that [tex]\lim_{x \to 0} \frac{sin x}{x} = 1[/tex]
    This limit is often proved by the "squeeze-play" theorem, but can be done other ways.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook