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anonymous
 3 years ago
prove that
Lim x>4 ((x4)/(2 (x)^1/2)) = 4
anonymous
 3 years ago
prove that Lim x>4 ((x4)/(2 (x)^1/2)) = 4

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dinnertable
 3 years ago
Best ResponseYou've already chosen the best response.4The easiest method is to use L'hopital's rule:\[\lim_{x \rightarrow 4} \frac{x4}{2\sqrt{x}} = \lim_{x \rightarrow 4} \frac{1}{\frac{1}{2}x^\frac{1}{2}} = \lim_{x \rightarrow 4}2\sqrt{x} = 4 \]The second, slightly longer method is to factor out the numerator as a difference of squares.\[\lim_{x \rightarrow 4} \frac{x4}{2\sqrt{x}} = \lim_{x \rightarrow 4} \frac{(\sqrt{x}  2)(\sqrt{x}+2)}{(\sqrt{x}  2)} = \lim_{x \rightarrow 4} (\sqrt{x} + 2) = 4\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0You 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.
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