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Math Help - Small Limit Problem

  1. #1
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    Small Limit Problem

    Hey, so I have this limit question, and I'm *pretty* sure that the limit does not exist, but I get my back up, because anyone could come to an answer like that from not knowing a way to simplify it. Can anyone see a way to simplify this and get a value?

    Thanks for any help!

    lim_{x->1}\frac{x^3+x^2}{x-1}

    Also, sorry for the dumb looking "approaches" arrow in the limit, I couldn't find the code for a good arrow in the LaTeX tutorial.
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  2. #2
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    Quote Originally Posted by Kasper View Post
    Hey, so I have this limit question, and I'm *pretty* sure that the limit does not exist, but I get my back up, because anyone could come to an answer like that from not knowing a way to simplify it. Can anyone see a way to simplify this and get a value?

    Thanks for any help!

    lim_{x->1}\frac{x^3+x^2}{x-1}

    Also, sorry for the dumb looking "approaches" arrow in the limit, I couldn't find the code for a good arrow in the LaTeX tutorial.
    lim_{x \rightarrow 1^+} \frac{x^3+x^2}{x-1} = + \infty

    lim_{x \rightarrow 1^-} \frac{x^3+x^2}{x-1} = - \infty

    Since the left hand and right hand limits are not equal, the limit does not exist.
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  3. #3
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    Ah right, I was looking at it all wrong. I keep trying to just simplify f(x) to find a way to sub in x and try to algebraically find an answer, I gotta start working on thinking of how the limit approaches rather than trying to find it when it's at the point in question.

    Thanks for the clarification!
    Last edited by Kasper; June 5th 2009 at 11:04 PM.
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