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Math Help - Limit Continuity

  1. #1
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    Limit Continuity

    check continuity at point
    Limit Continuity-forum.png

    Hello MHF, please help me with this exercise.
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  2. #2
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    Re: Limit Continuity

    A function is continuous at a point x if
    1) It is defined at that point.
    2) The function approaches the same value as you approach x from the left as it does when you approach x from the right.
    3) The function value is equal to this limiting value.
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  3. #3
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    Re: Limit Continuity

    The question's a little weird - I think you're probably supposed to take the limit of all three expressions as x goes to 0. Give each one a try and let us know how far you get. You'll probably need l'H˘pital's rule at a minimum.

    It probably doesn't help much, but for the second expression, you can take the limit as x goes to zero taking on only negative values, and for the third expression, you can take the limit as x goes to zero taking on only positive values.

    The first expression shouldn't have a limit - that's why I said the question was weird.

    - Hollywood
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  4. #4
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    Re: Limit Continuity

    I'm also thinking strange because the f(0) doesn't exist...
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