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Math Help - Continuity Problem

  1. #1
    Newbie Sterwine's Avatar
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    Continuity Problem

    I don't know how to do this question;

    Define the function f: R -> R by

    f(x)= { x^2 x>= 0
    { 0 x < 0

    Prove that f is continous.
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  2. #2
    MHF Contributor
    skeeter's Avatar
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    Quote Originally Posted by Sterwine View Post
    I don't know how to do this question;

    Define the function f: R -> R by

    f(x)= { x^2 x>= 0
    { 0 x < 0

    Prove that f is continous.
    1. show that f(0) is defined.

    2. show that \lim_{x \to 0} f(x) exists by comparing the one-sided limits from the left and the right of x = 0.

    3. show that \lim_{x \to 0} f(x) = f(0)
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