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Finding the value of a

  1. Jan 28, 2013 #1
    Finding the value of "a"

    1. The problem statement, all variables and given/known data
    Determine the value of "a" such that the function is continuous on the whole real line. You must clearly demonstrate why your choice of satisfies the definition of continuity


    2. Relevant equations

    f(x) = { (x+a), x≠a and 8, x=a


    3. The attempt at a solution

    x+a = 8
    a+a = 8
    2a=8
    a=4

    Then from there what do I do? Plug 4 into the first function?
    The 8, x=a --> is that undefined or limit does not exist?
     
  2. jcsd
  3. Jan 28, 2013 #2

    mfb

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    Re: Finding the value of "a"

    Right

    And show that the limit for x->4 is the same as the value at x=4. That can be done in 1-2 lines.
     
  4. Jan 28, 2013 #3
    Re: Finding the value of "a"

    x+a = 8
    x+4 = 8
    x=4?
     
  5. Jan 28, 2013 #4

    mfb

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    Re: Finding the value of "a"

    Those lines might need an explanation, but the general idea looks good.
     
  6. Jan 28, 2013 #5
    Re: Finding the value of "a"

    That's what I don't understand.

    I don't know how to explain the reasoning
    Because for the first function x≠a and for 8 x=a which makes since in regards to 4+4 = 8 since a=4 and x=a
     
  7. Jan 28, 2013 #6

    Mark44

    Staff: Mentor

    Re: Finding the value of "a"

    f(x) = x+a, if x≠a and 8, if x=a

    For f to be continuous at x = a, it must be true that f(a) = ##\lim_{x \to a} f(x)##

    So we must have ##\lim_{x \to a} f(x) = 8##
    ##\lim_{x \to a} f(x) = \lim_{x \to a} (x + a) = 2a##

    Hence 2a = 8, or a = 4.
     
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