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Math Help - continuity problem

  1. #1
    Junior Member mant1s's Avatar
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    continuity problem

    Hello Community,

    I am trying to solve this continuity problem and I might be doing something wrong... could someone please take a gander?

    Q: For what value of the constant c is the function f continous on ( -infn, infn) where...
    Code:
    piecewise function:
    
    f(x) = ct + 5   if t ε (-inf, 7]
             ct^2 - 5 if t ε (7, inf)
    I tried to solve for c but I think I missed a step. Here's what I did..

    Code:
    c(7) + 5 = c(7)^2 - 5
    7c + 5 = 14c - 5
    
    10/7 = c

    any help would be appreciated!
    Thx
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  2. #2
    MHF Contributor matheagle's Avatar
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    (7)^2 = 49, not 14.

    The idea is correct.
    You set the two parts equal to each other, so there isn't a jump.
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  3. #3
    Junior Member mant1s's Avatar
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    matheagle, thank you for pointing out my mistake!

    indeed 7^2 ≠ 14 haha

    solved answer is 5/21

    THANK YOU!
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  4. #4
    MHF Contributor matheagle's Avatar
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    It's good that you showed your work.
    Too many posters don't do that and it's hard for us to find the errors.
    We have no idea where you're stuck if we don't see your work.
    And no one should be afraid of making errors, we all do.
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