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Math Help - Determining continuity of function.

  1. #1
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    Determining continuity of function.

    I have a question on my homework that I'm not quite sure how to solve, the textbook as usual has no examples resembling this type of question, and its just been getting frustrating. Can anyone point me in the right direction? I'd really appreciate it! Thanks in advance!

    Determine the continuity if the function F(x) defined:

    F(x) = { 1 - x^2, x ≤ -1
    { 1 + x, -1 < x ≤ 1
    { x^2 + 2, x > 1
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  2. #2
    Junior Member
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    I think I got it,

    would it be discontinuous @ x = 1?

    because for y1:

    X = -1
    solving for 1- (x^2) gives me Y= 0

    y2:
    X=-1,1
    solving for 1+x gives me Y= 0,2

    y3:
    x=1
    solving for x^2 + 2 gives me Y = 3

    From those values can I say that it is discontinuous at x=1?
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  3. #3
    MHF Contributor
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    Hi

    \lim_{x\rightarrow 1^+} F(x) = \lim_{x\rightarrow 1^+} (x^2+2) because F(x) = x+2 over )1,+oo(

    \lim_{x\rightarrow 1^+} F(x) = 3

    And F(1) = 2 because F(x) = 1+x over )-1,1)

    Therefore \lim_{x\rightarrow 1^+} F(x) \neq F(1)

    which means that F is discontinuous at 1
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