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Math Help - Limits with infinity

  1. #1
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    Limits with infinity

    http://tinyurl.com/95xzk4d


    (a) lim f(x)
    x-> infinity

    (b) lim f(x)
    x-> - infinity

    (c) lim f(x)
    x->1

    (d) lim f(x)
    x-> 3

    (e) the equations of the asymptotes (Enter your answers as comma-separated lists.)

    Vertical?

    Horizontal?

    For infinity limits would is it the same left and right? Also how do you tell the vertical and horizontal asymptotes?
    Last edited by Oldspice1212; October 2nd 2012 at 09:40 PM.
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  2. #2
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    Re: Limits with infinity

    Err meant with infinity limits is it the same as in negative is left and positive is right.
    Last edited by Oldspice1212; October 3rd 2012 at 10:24 AM.
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    Re: Limits with infinity

    Positive infinity is "all the way" to the right, negative is "all the way" to the left.

    Spots where the line never touches, but always get closer and closer to, are asymptotes. An example of avertical asymptote would be on you graph at x=3. Notice the graph never touches it? Now, imagine the line going to the right, forever. It seems like it would never go past y=-2, that means that we have a horizontal asymptote at y=-2.
    Last edited by Nervous; October 3rd 2012 at 11:58 AM.
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  4. #4
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    Re: Limits with infinity

    What do you mean won't go past y= -2
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  5. #5
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    Re: Limits with infinity

    So, is a) -2 b)2 c)infinity d) - infinity and the asymptotes I have no clue about still.
    Last edited by Oldspice1212; October 4th 2012 at 11:41 AM.
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  6. #6
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    Re: Limits with infinity

    You got the limits right. I mean the line will never cross an asymptote. If I have a horizontal asymptote at x=2, the x value of the line will either always be higher than two, or lower than two, but it will never equal two. Think about the graph of \frac{3}{x-3} It would have a vertical asymptote at x=3, because if you plug 3 into the fraction, you would have \frac{3}{0} and that is an undefined fraction. So what points on your graph does the line never touch? Hint, the horizontal asymptotes are also limits.
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