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Help with continuity of functions

  1. Feb 14, 2012 #1
    1. The problem statement, all variables and given/known data

    For each of the following functions, find a value of a, (if such a value exists), which makes the function continuous.

    a) f(x) = {ax^2......x > 3
    ............{x - 7.......x ≤ 3

    b) f(x) = {sin(ax)....x < (pi)
    ............{1............x ≥ (pi)

    c) f(x) = {x^2 + a^2.....x > 1
    ............{9 - x.............x ≤ 1

    Does anyone know how to do these?
     
  2. jcsd
  3. Feb 15, 2012 #2

    tiny-tim

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    Science Advisor
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    Hi Cacophony! :smile:

    for (a), the only difficulty is at x = 3 …

    so put the two equations equal at x = 3 :wink:
     
  4. Feb 15, 2012 #3

    HallsofIvy

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    Staff Emeritus
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    Do you know the definition of "continuous"? That's a good place to start.
     
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