anonymous
  • anonymous
Find the limit lim x approaches infinity (sqrt9x^6-x)/(x^3+9)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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mathteacher1729
  • mathteacher1729
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?)
anonymous
  • anonymous
yes
anonymous
  • anonymous
3

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anonymous
  • anonymous
with your eyeballs.
anonymous
  • anonymous
here the numerator is not a polynomial, but think of it as one.
anonymous
  • anonymous
\[\sqrt{9x^6}=3x^3\]
anonymous
  • anonymous
so like you said earlier that the bigger the coeffienct is that the answer. so \[\sqrt{9x^6}= 3\]
anonymous
  • anonymous
now as we just saw you can ignore the lower stuff.
anonymous
  • anonymous
\[\frac{3x^3}{x^3}=3\] finished
anonymous
  • anonymous
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
anonymous
  • anonymous
but the textbook showed me a differnt answer
mathteacher1729
  • mathteacher1729
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.
anonymous
  • anonymous
better not have showed a different answer. maybe a different method, but not a different answer.
anonymous
  • anonymous
mathteacher wrote out all the details, but if i was doing it on an exam i would use my eyes
anonymous
  • anonymous
ok i will continut to show my professor this step to see if i can get credits thanks
anonymous
  • anonymous
good idea. that is the "proof" so write that out.

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