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anonymous

  • 4 years ago

evaluate the limit algebraically... lim x-->2 (x-2)/(sqrt(x)-sqrt(4-x))

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  1. anonymous
    • 4 years ago
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    \[\lim_{x\rightarrow 2}\frac{x-2}{\sqrt{x}-\sqrt{4-x}}\] like that?

  2. anonymous
    • 4 years ago
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    first make sure that, if you replace x by 2, you get 0/0, which you do. then multiply numerator and denominator by the conjugate of the denominator, i.e. multiply by \[\frac{\sqrt{x}+\sqrt{4-x}}{\sqrt{x}+\sqrt{4-x}}\]

  3. anonymous
    • 4 years ago
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    your new denominator will be \[2x-4=2(x-2)\] so you can cancel with the \[x-2\] in the numerator, leaving only \[\frac{\sqrt{x}+\sqrt{4-x}}{2}\] and now replace x by 2

  4. anonymous
    • 4 years ago
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    and don't kick out farmdawg, he doesn't like it

  5. anonymous
    • 4 years ago
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    haha what about a farmdawg? other than that thank you...

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