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Homework Help: 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.
     
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