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Finding A Constant To A Piece-Wise Function

  1. May 23, 2012 #1
    The function is g(x) = (x^2 - a^2)/(x - a) if x doesn't equal a; and the second part is g(x) = 8 when x = a. The question asks for me to find a specific value for a so that the function might be continuous on the entire real line.

    I know that each part of the piece-wise function needs to equal the same y-value, in order for their graphs to overlap; and, also, that the limit needs to approach the same value from each side of this point of possible discontinuity. Is that right? I am just not certain how to go about this. Could someone possibly prod me towards the correct route of solving this problem? Thank you.
     
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  3. May 23, 2012 #2

    micromass

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    So what must

    [tex]\lim_{x\rightarrow a} g(x)[/tex]

    be??
     
  4. May 23, 2012 #3
    Would it safe to presume that it would be 8? Also, what is this nonsense about receiving a warning? Is this not the calculus forum?
     
  5. May 23, 2012 #4

    micromass

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    Yes, so you must find a such that

    [tex]\lim_{x\rightarrow a} \frac{x^2-a^2}{x-a}=8[/tex]
     
  6. May 23, 2012 #5
    Oh, then that would properly satisfy the conditions of continuity--that g(a) exists, which it does, and the limits from both sides are equivalent to what the function is. Thank you very much. We really need a thank you button like that of the MathHelpForum's.
     
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