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Math Help - Help Needed with Advanced Limits

  1. #1
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    Help Needed with Advanced Limits

    I was wondering if someone could help me with the problems within the picture:




    I am in dire need of a step by step explanation as I answered this as Not enough info for #8 and -8 for #9 and both were incorrect
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  2. #2
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    well # 2 should be 8 since h(x) approaches 5, which causes g(x) to approach 8

    #1 is a piece wise function which is not continous since approaching the value from the right and left yield two different values
    i dont think you can answer this with the information your given
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  3. #3
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    Well #2 seems to be right, but if anyone could reword it, I'd be thankful. #1 can't be Not enough info because my proffesor said that that was the wrong answer. Any suggestions???
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  4. #4
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    Quote Originally Posted by TheUnfocusedOne View Post
    well # 2 should be 8 since h(x) approaches 5, which causes g(x) to approach 8

    #1 is a piece wise function which is not continous since approaching the value from the right and left yield two different values
    i dont think you can answer this with the information your given
    The right hand limit is (1)(4) = 4. The left hand limit is (-2)(-2) = 4. Left hand limit = right hand limit therefore the limit exists and is equal to

    Spoiler:
    *gasp* I can't believe it ...... 4
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  5. #5
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    Quote Originally Posted by TheUnfocusedOne View Post
    well # 2 should be 8 since h(x) approaches 5, which causes g(x) to approach 8
    I don't understand. It should approach -8 right? That's what I had thought but I was incorrect
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  6. #6
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    Quote Originally Posted by Some1Godlier View Post
    I don't understand. It should approach -8 right? That's what I had thought but I was incorrect
    \lim_{x \rightarrow p} g(h(x)) = g\left( \lim_{x \rightarrow p} h(x) \right)

    (provided certain conditions are met)

    = g(5).

    However, \lim_{u \rightarrow p} g(u) = g(5) only if g is continuous at u = 5. Since you have not been told whether or not this is the case, there is insufficient information to determine the given limit since the value of g(5) is not known.
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