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alfira

  • 3 years ago

help please!

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  1. across
    • 3 years ago
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    We're here to help.

  2. alfira
    • 3 years ago
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  3. alfira
    • 3 years ago
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    find the horzontal asymptotes

  4. across
    • 3 years ago
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    All you have to do is determine the behavior of \(f\) as it approaches both \(-\infty\) and \(\infty\), i.e.,\[\lim_{x\to\infty}\frac{x^2+3}{\sqrt{x^2+1}}=?\]

  5. alfira
    • 3 years ago
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    equal to 1 ?

  6. alfira
    • 3 years ago
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    y=1?

  7. across
    • 3 years ago
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    How did you get that?

  8. alfira
    • 3 years ago
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    x^2 / X^2 +3/x^2

  9. alfira
    • 3 years ago
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    everything divided by x^2

  10. alfira
    • 3 years ago
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    because highest power in the function is x^2

  11. across
    • 3 years ago
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    Recall that\[\lim_{x\to\infty}\frac{x^2+3}{\sqrt{x^2+1}}=\lim_{x\to\infty}\frac{x^2}{\sqrt{x^2}}=\lim_{x\to\infty}\frac{x^2}{|x|}=\lim_{x\to\infty}x=\infty.\]

  12. across
    • 3 years ago
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    So it has no horizontal asymptote as \(x\to\infty\). What about \(x\to-\infty\)?

  13. alfira
    • 3 years ago
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    same thing ?

  14. across
    • 3 years ago
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    Right.

  15. alfira
    • 3 years ago
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    thanks `

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