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Math Help - Limits Involving Radicals

  1. #1
    Newbie chili5's Avatar
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    Limits Involving Radicals

    Hello:

    I'm trying to evaluate this limit:

    <br />
lim       [(sqrt(7-x) - 2)/(sqrt(4-x)-1)]<br />
x->3 <br />

    but I'm having trouble getting started on this. I've tried rationalizing the numerator and denominator but doing that doesn't get me anywhere. Any thoughts??
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  2. #2
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    \dfrac{{\sqrt {7 - x}  - 2}}{{\sqrt {4 - x}  - 1}} = \dfrac{{\sqrt {4 - x}  + 1}}{{\sqrt {7 - x}  + 2}}

    That should work.
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  3. #3
    Newbie chili5's Avatar
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    Yea, that works. So you inverted the fraction but what is the rational behind changing - to +? How does that happen??
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  4. #4
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    Quote Originally Posted by chili5 View Post
    Yea, that works. So you inverted the fraction but what is the rational behind changing - to +? How does that happen??
    Multiply \frac{{\sqrt {7 - x}  - 2}}<br />
{{\sqrt {4 - x}  - 1}}\left( {\frac{{\sqrt {7 - x}  + 2}}<br />
{{\sqrt {7 - x}  + 2}}} \right)\left( {\frac{{\sqrt {4 - x}  + 1}}<br />
{{\sqrt {4 - x}  + 1}}} \right)
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