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robinfr93 Group Title

prove that Lim x->4 ((x-4)/(2 -(x)^1/2)) = -4

  • one year ago
  • one year ago

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  1. dinnertable Group Title
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    The easiest method is to use L'hopital's rule:\[\lim_{x \rightarrow 4} \frac{x-4}{2-\sqrt{x}} = \lim_{x \rightarrow 4} \frac{1}{-\frac{1}{2}x^\frac{-1}{2}} = \lim_{x \rightarrow 4}-2\sqrt{x} = -4 \]The second, slightly longer method is to factor out the numerator as a difference of squares.\[\lim_{x \rightarrow 4} \frac{x-4}{2-\sqrt{x}} = \lim_{x \rightarrow 4} \frac{(\sqrt{x} - 2)(\sqrt{x}+2)}{-(\sqrt{x} - 2)} = \lim_{x \rightarrow 4} -(\sqrt{x} + 2) = -4\]

    • one year ago
  2. Sir.GeorgeWashington Group Title
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    You Just Simply Can't Apply L'Hos.. rule to the Problem. You have to state the Criteria under which the Rule can be applied. With out the right condition, the Application of the Rule fails. All for Information and Guidance.

    • one year ago
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