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Math Help - Continuity help?

  1. #1
    Junior Member
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    Continuity help?

    I have a whole packet on continuity and i dont understand it at all. I have tried using my book but im at a loss. I have two questions one involving infinity.
    (6x-18)/(x^4-14x^3+49x^2) or 6x - 18 all over x to the 4th - 14x cubed + 49x squared
    Find each point of discontinuity of f and for each give the value of the point of discontinuity and evaluate the indicated one-sided limits.

    Evaluate the following limits
    lim as x approaches infinity (11-x)(9+7x) all over (3-8x)(5+10x)

    lim as x approaches negative infinity (11-x)(9+7x) all over (3-8x)(5+10x)

    please anyone who can help im not looking for the answers just a better understanding of how to solve for continuity.
    Thanks
    AC
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  2. #2
    MHF Contributor
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    A function written as f(x)/g(x) where both f(x) and g(x) are polynomials is discontinuous only at the points where g(x) = 0. So for the first question, you would solve for the denominator being equal to 0. It is clearly equal to 0 when x = 0, because you can factor out an x^2. To find the other points where it is equal to 0, solve the resulting quadratic equation.
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  3. #3
    Junior Member
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    continuity

    Ok so that makes since, where would dividing but the highest common value of x come into play?
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