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Math Help - Continuous functions help

  1. #1
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    Continuous functions help

    In the following question, k =0.5.






    I know how to prove the function but am unsure which part is the answer. Any help?

    -1 ≤ sin(1/2x) ≤ 1, for any x ≠ 0

    -xsqr ≤ xsqr sin(1/2x) ≤ xsqr, for any x ≠ 0

    g(x)[= -xsqr] ≤ f(x) ≤ [xsqr =]h(x), for any x ∈ ℝ

    As the functions satisfied all 3 conditions of the squeeze rule, f is continuous at 0.

    p/s: Sorry, i can't seem to get the square symbol working properly.
    Last edited by tottijohn; March 5th 2010 at 09:03 PM.
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  2. #2
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    the image is missing, you're gonna have to fix that.
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  3. #3
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    Fixed. Can you see it now?
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  4. #4
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    yes, it's right.
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  5. #5
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    Thanks.

    Anyone can help me out with this?
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  6. #6
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    haha, when i said that, i tacitly told you it's correct.
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  7. #7
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    Quote Originally Posted by Krizalid View Post
    haha, when i said that, i tacitly told you it's correct.
    Haha, thanks for clarifying.

    The qn here is asking for the lim f(x) which i am not sure.
    My lecturer said it is not 0.
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  8. #8
    Behold, the power of SARDINES!
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    Quote Originally Posted by tottijohn View Post
    Haha, thanks for clarifying.

    The qn here is asking for the lim f(x) which i am not sure.
    My lecturer said it is not 0.
    I think your lecturerer mispoke

    The function is not only continous at 0 by also differentiable as you proved by the squeeze theorem above the limit goes to zero.

    Here is a plot of the parabola's that bound the function in question.

    Continuous functions help-plot.jpeg
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  9. #9
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    So lim f(x) is really 0?

    Thanks for the detailed explanation!
    Not sure why my lecturer said it is not 0 though....
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