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Math Help - Continuity of hybrid function - Trying to find the value of c

  1. #1
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    Continuity of hybrid function - Trying to find the value of c

    Did I do this correct?

    determine the values of c such that the function f is continuous on the entire real line

    f(x)={x+3 if x less than or equal to 2
    cx+6 if x>2


    lim x->2+ cx+6=2c+6

    lim x->2- x+3=5

    2c+6=5
    -6 -6
    2c/2=-1/2

    c=-1/2
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  2. #2
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    Re: Trying to find the value of c

    Quote Originally Posted by LAPOSH42 View Post
    Did I do this correct?

    determine the values of c such that the function f is continuous on the entire real line

    f(x)={x+3 if x less than or equal to 2
    cx+6 if x>2


    lim x->2+ cx+6=2c+6

    lim x->2- x+3=5

    2c+6=5
    -6 -6
    2c/2=-1/2

    c=-1/2
    That is correct.

    Here is some simple LaTeX code
    [TEX]\lim _{x \to 2^ + } f(x) = 2c + 6[/TEX] gives \lim _{x \to 2^ +  } f(x) = 2c + 6
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