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Math Help - limits and continuity problem

  1. #1
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    Question limits and continuity problem

    1. given: limits and continuity problem-untitled.png

    need to find all the constants c for which the function is continuous in the section (-oo,+oo).


    2.given: limits and continuity problem-untitle1d.png calculate the limit of limits and continuity problem-untitle2d.png (ignore the marks), from what i calculated it's supposed to be 17.2 but i think it's wrong somehow.
    also need to prove that g(x) isn't continuous in the section (-oo,+oo)

    I have tried for more than an hour to solve these and I am very frustrated by now.

    appreciate your help, thanks.
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  2. #2
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    Re: limits and continuity problem

    Quote Originally Posted by ryu1 View Post
    1. given: Click image for larger version. 

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ID:	27555
    need to find all the constants c for which the function is continuous in the section (-oo,+oo).
    2.given: Click image for larger version. 

Name:	Untitle1d.png 
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ID:	27556 calculate the limit of Click image for larger version. 

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ID:	27557 .
    For the first solve |2+c|=1.

    For the second, just note that \lim _{x \to \infty }}g(x) =  - 4
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  3. #3
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    Re: limits and continuity problem

    For the first I did solved that c must be -1 but I get confused that the instructions asks to "find ALL the possible c constants..." as if there's more than one?

    For the second I did figured that out but it is right to place -4 in the limit problem later? like
    g(x) = -4 so 10*(-4)^2 -3(-4) / 6 - (-4)

    From that I got to 172/10. is that right?

    Thanks a lot!
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  4. #4
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    Re: limits and continuity problem

    Quote Originally Posted by ryu1 View Post
    For the first I did solved that c must be -1 but I get confused that the instructions asks to "find ALL the possible c constants..." as if there's more than one?

    For the second I did figured that out but it is right to place -4 in the limit problem later? like
    g(x) = -4 so 10*(-4)^2 -3(-4) / 6 - (-4)

    From that I got to 172/10. is that right?
    Yes, the second is correct.

    But for the first, c=-1\text{ or }c=-3.
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  5. #5
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    Re: limits and continuity problem

    Quote Originally Posted by Plato View Post
    Yes, the second is correct.

    But for the first, c=-1\text{ or }c=-3.
    Oh to solve the absolute value problem I need to:
    One time calculate c assuming the expression inside the absolute value is positive (aka leaving it as it is).
    And once more assuming it is negative (because the absolute value will negate the minus sign) which makes it -(2+c) = -2-c = 1 = c = -3 ?


    How to prove that g(x) is not continuous in the section (-oo,+oo) ?
    need to find g(x) = 6 so that I'd get a 0 in the denominator for that x?



    Thanks a lot.
    I have 6 problems I need to send out part of calculus course and I have been sitting on them for 4 hours making little progress (only answered about 3 ).
    Last edited by ryu1; March 16th 2013 at 03:17 PM.
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