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alfira Group Title

help please!

  • one year ago
  • one year ago

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  1. across Group Title
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    We're here to help.

    • one year ago
  2. alfira Group Title
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    • one year ago
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  3. alfira Group Title
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    find the horzontal asymptotes

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

    • one year ago
  5. alfira Group Title
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    equal to 1 ?

    • one year ago
  6. alfira Group Title
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    y=1?

    • one year ago
  7. across Group Title
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    How did you get that?

    • one year ago
  8. alfira Group Title
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    x^2 / X^2 +3/x^2

    • one year ago
  9. alfira Group Title
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    everything divided by x^2

    • one year ago
  10. alfira Group Title
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    because highest power in the function is x^2

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

    • one year ago
  12. across Group Title
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    So it has no horizontal asymptote as \(x\to\infty\). What about \(x\to-\infty\)?

    • one year ago
  13. alfira Group Title
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    same thing ?

    • one year ago
  14. across Group Title
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    Right.

    • one year ago
  15. alfira Group Title
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    thanks `

    • one year ago
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