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Math Help - Limit values?

  1. #1
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    Limit values?

    I was given a calculus assignment, and don't quite get what the teacher meant. Any aid is appreciated.

    f(x){X^2 X less than or equal to 2
    8-2x for 2 < X< 4
    4 for X> or equal to 4}


    Identify the values of c for which the lim x approaches c of f(x) exist.

    What is c, what does this mean?
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  2. #2
    MHF Contributor
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    West Malaysia
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    Quote Originally Posted by GOPgabe View Post
    I was given a calculus assignment, and don't quite get what the teacher meant. Any aid is appreciated.

    f(x){X^2 X less than or equal to 2
    8-2x for 2 < X< 4
    4 for X> or equal to 4}


    Identify the values of c for which the lim x approaches c of f(x) exist.

    What is c, what does this mean?
    You are supposed to find the point c where the graph is continuous. One way is to sketch the graph and you will see that the graph is continuous at x=2. To prove it,

    take limits as x approaches 2^- and 2^+, and also calculate f(2).

    If \lim_{x\rightarrow 2^-}=\lim_{x\rightarrow 2^+}=f(2)

    Then the graph is continuous at x=2.
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