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Math Help - Easly limit problem dont know how to start

  1. #1
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    Easly limit problem dont know how to start

    Could any body please give me a hint about the first step

    Find \lim_{x \to 2} \left[ \frac{x-1}{x-2} - \frac{1}{ln(x-1)} \right]
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  2. #2
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    The difficulty with a question like this, where you show no work at all, is that we have no idea what you have available. Since this is of the form " \infty- \infty", I would be inclined to combine the fractions, changing it into a "0/0" situation, then use L'Hopital's rule.
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  3. #3
    Senior Member Shanks's Avatar
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    just as what HallsofIvy said, next time you should show your effort in your post, then we can help you in a better and more efficient way.
    \lim_{x\to 2}(\frac{x-1}{x-2}-\frac{1}{ln(x-1)})<br />
=\lim_{x\to 2}\frac{(x-1)ln(x-1)-x+2}{(x-2)ln(x-1)}
    =\lim_{x\to 2}\frac{ln(x-1)+1-1}{ln(x-1)+\frac{x-2}{x-1}} (Hopital's rule)
    =\lim_{x\to 2}\frac{(x-1)ln(x-1)}{(x-1)ln(x-1)+x-2}
    =\lim_{x\to 2}\frac{ln(x-1)+1}{ln(x-1)+1+1} (Hopital's rule again!)
    =\frac{1}{2}.
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by HallsofIvy View Post
    The difficulty with a question like this, where you show no work at all, is that we have no idea what you have available. Since this is of the form " \infty- \infty", I would be inclined to combine the fractions, changing it into a "0/0" situation, then use L'Hopital's rule.
    To get an idea of what the OP knows see zorro's posts. The OP and zorro are one and the same.

    CB
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