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Math Help - Continuity question

  1. #1
    Newbie Sterwine's Avatar
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    Continuity question

    So, the question asks; If F(x) = x^2sin(π/x), prove that f(0) can be defined in such a way that f becomes continous at x = 0.

    I know for continuity you need to prove that the limit F(x) exists. So I used the squeeze theroem and found that the limit as x approaches 0 is 0.

    I am having trouble proving that f(0) is defined. I know this is probably a stupid question but I just hit a math road block.

    Thanks for your help!
    -Sterwine
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  2. #2
    MHF Contributor
    skeeter's Avatar
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    Quote Originally Posted by Sterwine View Post
    So, the question asks; If F(x) = x^2sin(π/x), prove that f(0) can be defined in such a way that f becomes continous at x = 0.

    I know for continuity you need to prove that the limit F(x) exists. So I used the squeeze theroem and found that the limit as x approaches 0 is 0.

    I am having trouble proving that f(0) is defined. I know this is probably a stupid question but I just hit a math road block.

    Thanks for your help!
    -Sterwine
    -x^2 \le x^2\sin\left(\frac{\pi}{x}\right) \le x^2

    y = -x^2 and y = x^2 both equal 0 at x = 0

    the question is not asking you to prove if f(0) is defined at x = 0, it isn't ... yet.
    the question is asking how you would define f(0) to make the function continuous.

    why do you think they call it a "removable" discontinuity?
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  3. #3
    Newbie Sterwine's Avatar
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    Ah, thats exactly what I got, I guess I was just confused and read the question wrong.

    Thank you very much
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