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find the horzontal asymptotes

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Other answers:

All you have to do is determine the behavior of \(f\) as it approaches both \(-\infty\) and \(\infty\), i.e.,\[\lim_{x\to\infty}\frac{x^2+3}{\sqrt{x^2+1}}=?\]
equal to 1 ?
y=1?
How did you get that?
x^2 / X^2 +3/x^2
everything divided by x^2
because highest power in the function is x^2
Recall that\[\lim_{x\to\infty}\frac{x^2+3}{\sqrt{x^2+1}}=\lim_{x\to\infty}\frac{x^2}{\sqrt{x^2}}=\lim_{x\to\infty}\frac{x^2}{|x|}=\lim_{x\to\infty}x=\infty.\]
So it has no horizontal asymptote as \(x\to\infty\). What about \(x\to-\infty\)?
same thing ?
Right.
thanks `

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