1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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.
  2. jcsd
  3. May 23, 2012 #2
    So what must

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

  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
    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook