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Math Help - Limit help.

  1. #1
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    Limit help.

    What is the limit of:


    lim \pi x cos(\frac{1}{3 \pi x})
    x->0


    My teacher said that what is inside of cosine is limited so  cos(\frac{1}{3 \pi x})[TEX] it doesnt "metter"...

    and limit when  x -> 0 = \pi 0  =  0


    Can you explain me why the it "doesnt metter"
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  2. #2
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    Re: Limit help.

    Quote Originally Posted by Fabio010 View Post
    What is the limit of:


    lim \pi x cos(\frac{1}{3 \pi x})
    x->0


    My teacher said that what is inside of cosine is limited so  cos(\frac{1}{3 \pi x})[TEX] it doesnt "metter"...

    and limit when  x -> 0 = \pi 0  =  0


    Can you explain me why the it "doesnt metter"
    as x gets closer to 0, \frac{1}{3\pi \cdot x} becomes a very large value ... yet, -1 \le \cos(any \, value) \le 1

    so, what you have is ...

    \lim_{x \to 0} \pi x (some \, value \, between \, -1 \, and \, 1)

    understand why the limit is 0?
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  3. #3
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    Re: Limit help.

    Understood.

    Thanks for the help.!
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  4. #4
    Grand Panjandrum
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    Re: Limit help.

    Quote Originally Posted by Fabio010 View Post
    What is the limit of:


    lim \pi x cos(\frac{1}{3 \pi x})
    x->0


    My teacher said that what is inside of cosine is limited so  cos(\frac{1}{3 \pi x})[TEX] it doesnt "metter"...

    and limit when  x -> 0 = \pi 0  =  0


    Can you explain me why the it "doesnt metter"
    Squeeze theorem:

    -\pi x \le \pi x \cos\left(\frac{1}{3\pi x} \right) \le \pi x

    CB
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