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anonymous

  • 5 years ago

Find the limit lim x approaches infinity (sqrt9x^6-x)/(x^3+9)

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  1. mathteacher1729
    • 5 years ago
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    do you mean \[\lim_{x\to \infty} \frac{\sqrt{9x^6-x}}{x^3+9}\] ? (Is that the placement of the square root and the stuff under it?)

  2. anonymous
    • 5 years ago
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    yes

  3. anonymous
    • 5 years ago
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    3

  4. anonymous
    • 5 years ago
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    with your eyeballs.

  5. anonymous
    • 5 years ago
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    here the numerator is not a polynomial, but think of it as one.

  6. anonymous
    • 5 years ago
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    \[\sqrt{9x^6}=3x^3\]

  7. anonymous
    • 5 years ago
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    so like you said earlier that the bigger the coeffienct is that the answer. so \[\sqrt{9x^6}= 3\]

  8. anonymous
    • 5 years ago
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    now as we just saw you can ignore the lower stuff.

  9. anonymous
    • 5 years ago
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    \[\frac{3x^3}{x^3}=3\] finished

  10. anonymous
    • 5 years ago
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    think of it as the rules we just wrote. even though this is not one polynomial over another you can pretend it is. then the degrees are the same and 3/1=3

  11. anonymous
    • 5 years ago
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    but the textbook showed me a differnt answer

  12. mathteacher1729
    • 5 years ago
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    Start by dividing everything in the numerator and everything in the denominator by x^3. This gives: \[\lim x \to \infty \frac{\frac{1}{x^3}\sqrt{9x^6-x}}{\frac{1}{x^3}(x^3+9)} \] Distribute the x^3 appropriately and we have... \[\lim_{x \to \infty} \frac{\sqrt{\frac{9x^6}{x^6}-\frac{x}{x^3}}}{(\frac{x^3}{x^3}+\frac{9}{x^3})} \] and this simplifies (thank heavens) to : \[\lim_{x \to \infty} \frac{\sqrt{9-\frac{1}{x^2}}}{1+\frac{9}{x^3}}\] As x goes to infinity this limit becomes: \[\frac{\sqrt{9-0}}{1}=3\] And that's your answer. Wooo.

  13. anonymous
    • 5 years ago
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    better not have showed a different answer. maybe a different method, but not a different answer.

  14. anonymous
    • 5 years ago
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    mathteacher wrote out all the details, but if i was doing it on an exam i would use my eyes

  15. anonymous
    • 5 years ago
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    ok i will continut to show my professor this step to see if i can get credits thanks

  16. anonymous
    • 5 years ago
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    good idea. that is the "proof" so write that out.

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