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anonymous
 5 years ago
compute limit x>3 x^481/2x^25x3
anonymous
 5 years ago
compute limit x>3 x^481/2x^25x3

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[(x^{4}81)/(2x ^{2}5x3)\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0you asking for the limit of that is it goes to 3?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0You have something called an 'indeterminate form' since both the numerator and denominator approach 0 as x approaches 3. In these cases, you can use L'Hopital's rule, which says\[\lim_{x \rightarrow a}\frac{f(x)}{g(x)}=\lim_{x \rightarrow a}\frac{f'(x)}{g'(x)}\]In your case, \[\lim_{x \rightarrow 3}\frac{x^481}{2x^25x3}=\lim_{x \rightarrow 3}\frac{4x^3}{4x5}=\frac{108}{7}\]
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