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Thread: Limits

  1. #1
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    Question Limits

    Hey guys so I have no idea how to solve limits while looking at a graph, here is the image...


    lim
    t 0
    g(t)


    lim
    t 0+
    g(t)



    lim
    t 0
    g(t)

    lim
    t 2
    g(t)

    lim
    t 2+
    g(t)


    lim
    t 2
    g(t)




    g(2)



    lim
    t 4
    g(t)



    Last edited by Oldspice1212; Sep 20th 2012 at 07:59 AM.
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  2. #2
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    Re: Limits

    Quote Originally Posted by Oldspice1212 View Post

    lim
    t 0
    g(t)


    lim
    t 0+
    g(t)



    lim
    t 0
    g(t)

    lim
    t 2
    g(t)

    lim
    t 2+
    g(t)


    lim
    t 2
    g(t)




    g(2)



    lim
    t 4
    g(t)



    The answer to the first is $\displaystyle -1$.

    The answer to the second is $\displaystyle -2$.

    You figure out why. Then do the others and report the answers you get.
    We will be glad to help you then.
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  3. #3
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    Re: Limits

    So for the third one it would be 2 since from the right it goes towards 2 and from left closest is to the 2?

    fourth -2?
    fifth 1
    sixth 2
    7th no idea
    8th - 3?
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  4. #4
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    Re: Limits

    Hello, Oldspice1212!

    Here's part of the solution . . .


    I have no idea how to solve limits while looking at a graph.
    Do you understand "from the left" and "from the right"?
    You just trace it with your finger.
    Code:
              |
             4+                  *
              |                 *
             3+               ♥
         *    |             *
             2+       o    *
              |      *    *
          *  1+     * ♥  *
              |    *    *
        - -*- + - * - o - + - + - -
            * |  *1   2   3   4
            -1♥ *
              |*-
            -2o
              |
    $\displaystyle (1)\;\lim_{t\to0^-}g(t)$
    As $\displaystyle t$ approahes 0 from the left, $\displaystyle g(x)$ approaches $\displaystyle \text{-}1.$
    Hence: .$\displaystyle \lim_{t\to0^-}g(t) \:=\:\text{-}1$


    $\displaystyle (2)\;\lim_{t\to0^+}g(t)$
    As $\displaystyle t$ approaches 0 from the right, $\displaystyle g(t)$ approaches $\displaystyle \text{-}2.$
    Hence: .$\displaystyle \lim_{t\to0^+}g(t) \:=\:\text{-}2$


    $\displaystyle (3)\;\lim_{t\to0}g(t)$
    Does not exist.


    $\displaystyle (4)\;\lim_{t\to2^-}g(t)$
    As $\displaystyle t$ approaches 2 from the left, $\displaystyle g(t)$ approaches $\displaystyle 2.$
    Hence: .$\displaystyle \lim_{t\to2^-}g(t) \:=\:2$


    $\displaystyle (5)\;\lim_{t\to2^+}g(t)$
    As $\displaystyle t$ approaches 2 from the right, $\displaystyle g(t)$ approaches 0.
    Hence: .$\displaystyle \lim_{t\to2^+}g(t) \:=\:0$


    $\displaystyle (6)\;\lim_{t\to2}g(t)$
    Does not exist.


    $\displaystyle (7)\;g(2)$
    $\displaystyle g(2) \:=\: 1$

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  5. #5
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    Re: Limits

    Oh wow thank you so much!! The explanations on approaching helped a ton.
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  6. #6
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    Re: Limits

    Quick question for lim g(t)
    t - 4

    would this = 0 or DNE?
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