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Continuous Function Problems AP Calculus

  1. Sep 21, 2009 #1
    1. The problem statement, all variables and given/known data
    Let f be the function given by f(x)= (x-1)(x²-4)/ (x²-a). For What Positive Values of a is f continuous for all real numbers x?


    2. Relevant equations



    3. The attempt at a solution
    What I tried doing was separating the (x²-4) into (x+2)(x-2) then moving along from there, but I can't seem to figure out what number a can be without having a discontinuity.

    Thanks for trying!
    Loppyfoot
     
  2. jcsd
  3. Sep 21, 2009 #2

    LCKurtz

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    Hint:

    1. Are polynomials continuous?
    2. Are products of continuous functions continuous?
    3. Are quotients of continuous continuous?

    Are any of the answers above valid for all values of x or are any of them subject to some "if" conditions?
     
  4. Sep 21, 2009 #3
    So Then, I would guess a=4, because the the (x²-4) and the (x²-4) cancel out and you are left with (x-1).
     
  5. Sep 21, 2009 #4

    LCKurtz

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    You aren't permitted to cancel anything out since that makes minor changes in the function. Try answering the three questions I posed. That might lead you to the solution.
     
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