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Homework Help: Undefined functions and limits

  1. Apr 16, 2010 #1
    1. The problem statement, all variables and given/known data

    The function f is defined by f(x)=(3sin(2x^2))/x^2 , x<0 . Find limit f(x) when x approaches 0 .

    2. Relevant equations



    3. The attempt at a solution

    Of course , when i plug 0 in, f(x) is undefined . How do i make into a form where i can plug the 0 in without the function being undefined
     
  2. jcsd
  3. Apr 16, 2010 #2
    Re: limits

    Well, I assume you know what [tex] \lim\limits_{x \to 0} \frac{sinx}{x} [/tex] is. That applies to x being more complex than a single number as well.
    More generally, my suggestion is to read about de L'Hospital's rule that allows you to calculate limes when you encounter the situation [tex] \frac{0}{0} [/tex] or [tex] \frac{\infty}{\infty} [/tex].
     
  4. Apr 16, 2010 #3
    Re: limits

    ok , i will try to read up that rule but is there any elementary method to evaluate the limit for that function ?
     
  5. Apr 16, 2010 #4

    Cyosis

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    Homework Helper

    Re: limits

    Can you write down the derivative of sin(x) by using the definition of the derivative? Compare this to the limit you're asked to compute.
     
  6. Apr 16, 2010 #5

    HallsofIvy

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    Re: limits

    If you are referring to [itex]\lim_{x\to 0} sin(x)/x[/itex], how you prove that depends on exactly how you are defining sin(x).
     
  7. Apr 16, 2010 #6
    Re: limits

    you meant this :

    [tex]f'(x)=\lim_{\delta x\rightarrow 0}(\frac{\sin (x+\delta x)-\sin x}{\delta x})[/tex] ?
     
  8. Apr 16, 2010 #7

    Cyosis

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    Re: limits

    Yes, how can you modify that expression so that it is equal to your limit problem?
     
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