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Math Help - Singularities or discontinuities

  1. #1
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    Singularities or discontinuities

    ok I have understand how to do it but i ave confuse when is removable and when is non-removable

    here is the question:
    Find any singularities or discontinuities in the following functions:

    f(x)=(x+3)/(x^2-9)
    (an:non-removable singularity at x=3, removable singularity at x=-3, put f(x)=-1/6)

    f(x)=cosx/(x-π/2)
    (an:removabe singularity at x=π/2, put f(π/2)=-1)
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  2. #2
    MHF Contributor Calculus26's Avatar
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    A discontinuity is removable if the limit exists

    Remember Continuity means lim x->a f(x) = f(a)

    which implies
    1. f(a) is defined
    2. lim x->a f(x)
    3. 1 = 2

    For example

    f(x)=(x+3)/(x^2-9)

    limas x->-3 = -1/6 so if we define f(-3) =-1/6 all conditions are met

    limasx->3 DNE fails 2 cannot remove discontinuity
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  3. #3
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    why the lim x->3= -1/6!???!?i found it -infinite
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  4. #4
    MHF Contributor Calculus26's Avatar
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    Re read the post I said lim x-> -3 = -1/6

    and lim x-> 3 DNE
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  5. #5
    Behold, the power of SARDINES!
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    Quote Originally Posted by NaNa View Post
    ok I have understand how to do it but i ave confuse when is removable and when is non-removable

    here is the question:
    Find any singularities or discontinuities in the following functions:

    f(x)=(x+3)/(x^2-9)
    (an:non-removable singularity at x=3, removable singularity at x=-3, put f(x)=-1/6)

    f(x)=cosx/(x-π/2)
    (an:removabe singularity at x=π/2, put f(π/2)=-1)
    The simple idea is that if f(x) is undefined at a point x_0 but the limit at the point \lim_{x \to x_0}f(x)=c < \infty the we can extend the function to the value c at x_0 ie f(x_0)=c

    Edit: Geez I am really late
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  6. #6
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    i find the same answer!?
    where do you subtract the limit?!
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  7. #7
    MHF Contributor Calculus26's Avatar
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    I'm not sure what you mean by " subtract the limit" ?
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  8. #8
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    Hmm is ok I have understand
    thanks a lot!
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