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Math Help - Does the limit exist?

  1. #1
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    Does the limit exist?

    Please help me with this limit problem:

    limit as x approaches 1 of: (x^4-1)/(x^3-1)

    I factored the top to be (x^2-1)(x^2+1) and the bottom using difference of cubes which I got to be (x-1)(x^2+x+1)

    I am stuck at this point because nothing seems to cancel out and I dont see any more factors. So does it not exist?
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  2. #2
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    Re: Does the limit exist?

    Quote Originally Posted by jmanna98 View Post
    Please help me with this limit problem:

    limit as x approaches 1 of: (x^4-1)/(x^3-1)

    I factored the top to be (x^2-1)(x^2+1) and the bottom using difference of cubes which I got to be (x-1)(x^2+x+1)

    I am stuck at this point because nothing seems to cancel out and I dont see any more factors. So does it not exist?
    \displaystyle \begin{align*} \frac{x^4 - 1}{x^3 - 1} &= \frac{(x^2 - 1)(x^2 + 1)}{(x - 1)(x^2 + x + 1)} \\ &= \frac{(x - 1)(x + 1)(x^2 + 1)}{(x - 1)(x^2 + x + 1)} \\ &= \frac{(x + 1)(x^2 + 1)}{x^2 + x + 1} \end{align*}

    Now make \displaystyle x \to 1.
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