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Math Help - show that f(x) has a removable discontinuity...

  1. #1
    Member dokrbb's Avatar
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    show that f(x) has a removable discontinuity...

    I have the function f(x) equal to 3/x+(-2x + 6)/[x(x-2)] when x different to 0, and 2,

    and f(x) equals 9 when x = 0

    I have to show that f(x) has a removable discontinuity at x=0

    I'm stucked with the transformation of these fractions and it leads me nowhere, can you show me please the first few steps?

    I also tried to put it in LaTeX but I got something wrong, (see below)

    [tex]f(x)=\left\{\begin{array}{\frac{3}{x}+\frac{-2x + 6}{x(x-2)}}, &\mbox{ if }\x \ne 0, 2\\9, & \mbox{if}x=0\end{array}\right[tex]
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  2. #2
    Member agentmulder's Avatar
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    Re: show that f(x) has a removable discontinuity...

    Quote Originally Posted by dokrbb View Post
    I have the function f(x) equal to 3/x+(-2x + 6)/[x(x-2)] when x different to 0, and 2,

    and f(x) equals 9 when x = 0

    I have to show that f(x) has a removable discontinuity at x=0

    I'm stucked with the transformation of these fractions and it leads me nowhere, can you show me please the first few steps?

    I also tried to put it in LaTeX but I got something wrong, (see below)

    f(x)=\left\{\begin{array}{\frac{3}{x}+\frac{-2x + 6}{x(x-2)}}, &\mbox{ if }\x \ne 0, 2\\9, & \mbox{if}x=0\end{array}\right

    If the limit from the left of zero is equal to the limit from the right of zero AND that limit is a finite number then the function will have a removeable discontinuity. Calculate the 1 sided limits as x--> 0

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  3. #3
    Forum Admin topsquark's Avatar
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    Re: show that f(x) has a removable discontinuity...

    Try
    [tex]f(x)=\begin{cases}{\frac{3}{x}+\frac{-2x + 6}{x(x-2)}}, &\mbox{ if }x \ne 0, 2\\9, & \mbox{ if }x=0\end{cases}\right[/tex]

    It comes out as
    f(x)=\begin{cases}{\frac{3}{x}+\frac{-2x + 6}{x(x-2)}}, &\mbox{ if }x \ne 0, 2\\9, & \mbox{ if }x=0\end{cases}\right

    I don't recall how to center the 9.

    -Dan
    Last edited by topsquark; April 7th 2013 at 10:16 PM.
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  4. #4
    Member dokrbb's Avatar
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    Re: show that f(x) has a removable discontinuity...

    Thanks to both of you - I've got the answer, It's \frac{1}{-2}
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