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Math Help - An indeterminate limit question

  1. #1
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    An indeterminate limit question

    Suppose lim x→1 (sqrt(ax+b)-2)/(x-1)=1, then a-b = ?

    The answer key solved this by seeing the limit as 0/0, and therefore, sqrt(ax+b)-2 as 0.
    What's the assumption, sqrt(ax+b)-2=0, based on?

    Thanks in advance!
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  2. #2
    MHF Contributor Siron's Avatar
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    Re: An indeterminate limit question

    If you substitute the value x=1 in the limit then the denominator is equal to 0. This means the numerator can't be equal to some L \in \mathbb{R}\setminus \{0\} as the limitvalue would be infinite then (i.e it would not exist). Hence the only possibility is that the numerator is equal to 0 as \frac{0}{0} is undefined.
    Last edited by Siron; March 22nd 2013 at 09:26 AM.
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