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Math Help - finding limits

  1. #1
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    finding limits

    if f(x)={2-x, x<-1
    x, -1<=x<1
    (x-1)^2, x>=1}

    find limit (f(x), x, -1-)
    limit (f(x), x, -1+)

    I have graphed the functions above but do not know how to find the limits, can someone please explain the steps needed?

    Thanks!
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  2. #2
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    \underset{x\to -1^{-}}{\mathop{\lim }}\,(2-x) and \underset{x\to -1^{+}}{\mathop{\lim }}\,x, got it?
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  3. #3
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    No, because I don't even know how to start finding limits. I have seen them written this way, but I don't know what it means. I don't care if you solve my particular problem, but if you could just show me some kind of example I could follow, it would be very helpful!
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by sjenkins View Post
    No, because I don't even know how to start finding limits. I have seen them written this way, but I don't know what it means. I don't care if you solve my particular problem, but if you could just show me some kind of example I could follow, it would be very helpful!
    \lim_{x \to -1^-} \cdots means "the limit as x tends to -1 from the left of ..."

    \lim_{x \to -1^+} \cdots means "the limit as x tends to -1 from the right of ..."

    so when it asks \lim_{x \to -1^-}f(x), you say, okay, i am coming from the left of -1, that means, i want the function as it is defined for x < -1, because those are the values to the left of -1. now i look at my function and realize that for x < -1, the function is 2 - x

    so i want \lim_{x \to -1^-} (2 - x)

    this function is continuous, so you can just plug in -1 to find the limit.

    \lim_{x \to -1^-} (2 - x) = 2 - (-1) = 3

    a similar story holds true for the other one-sided limit
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  5. #5
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    Thank you, I can finally understand that. I really appreciate the help!
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