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alfira
 2 years ago
Best ResponseYou've already chosen the best response.0find the horzontal asymptotes

across
 2 years ago
Best ResponseYou've already chosen the best response.0All you have to do is determine the behavior of \(f\) as it approaches both \(\infty\) and \(\infty\), i.e.,\[\lim_{x\to\infty}\frac{x^2+3}{\sqrt{x^2+1}}=?\]

alfira
 2 years ago
Best ResponseYou've already chosen the best response.0everything divided by x^2

alfira
 2 years ago
Best ResponseYou've already chosen the best response.0because highest power in the function is x^2

across
 2 years ago
Best ResponseYou've already chosen the best response.0Recall that\[\lim_{x\to\infty}\frac{x^2+3}{\sqrt{x^2+1}}=\lim_{x\to\infty}\frac{x^2}{\sqrt{x^2}}=\lim_{x\to\infty}\frac{x^2}{x}=\lim_{x\to\infty}x=\infty.\]

across
 2 years ago
Best ResponseYou've already chosen the best response.0So it has no horizontal asymptote as \(x\to\infty\). What about \(x\to\infty\)?
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