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!

Help finding a limit

  1. May 19, 2008 #1
    1. The problem statement, all variables and given/known data
    [tex]\mathop {\lim }\limits_{x \to 0} (1 - \cos x)[/tex]

    2. The attempt at a solution

    well as x goes to 0, cos x goes to 1... ln(1-1) is undefined
    now if I forget about plugging in x=0 and think a little bit, the ln argument gets very very small, and the logarithm of a decimal number is a negative number... so I would say the limit is minus infinity.

    however, is it possible to get that result analytically.... by transforming/simplyfing/etc. the function?

    sorry, I have just finished precalculus and I am beginning calculus, so my calculus skills are crap =\

    thank you
    Last edited: May 19, 2008
  2. jcsd
  3. May 19, 2008 #2
    hmm ... problem is: [tex]\lim_{x\rightarrow0}(1-\cos x)[/tex]?

    Can't you just plug it in?

    Or is it:

    [tex]\lim_{x\rightarrow0}\ln{(1-\cos x)}[/tex]

    Ok so have the graph infront of you. You know as you "approach" coming from the right, it's negative infinity ...

    [tex]\lim_{x\rightarrow0^{+}}\ln{(1-\cos x)}=-\infty[/tex]

    What about from the left? Because in order for the Limit to exist, the L & R Limits must agree. But for the natural logarithm, how is it uniquely defined?
    Last edited: May 19, 2008
  4. May 20, 2008 #3
    Once you have learned L^Hopitals rule, you will be able to apply it to this equation and get the same answer analytically.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Help finding a limit
  1. Finding a limit help. (Replies: 12)

  2. Help me find a limit! (Replies: 4)

  3. Help find this limit. (Replies: 3)

  4. Finding a limit help. (Replies: 4)