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anonymous
 5 years ago
Find the limit
lim x approaches infinity (sqrt9x^6x)/(x^3+9)
anonymous
 5 years ago
Find the limit lim x approaches infinity (sqrt9x^6x)/(x^3+9)

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mathteacher1729
 5 years ago
Best ResponseYou've already chosen the best response.0do you mean \[\lim_{x\to \infty} \frac{\sqrt{9x^6x}}{x^3+9}\] ? (Is that the placement of the square root and the stuff under it?)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0here the numerator is not a polynomial, but think of it as one.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so like you said earlier that the bigger the coeffienct is that the answer. so \[\sqrt{9x^6}= 3\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0now as we just saw you can ignore the lower stuff.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[\frac{3x^3}{x^3}=3\] finished

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0think 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
 5 years ago
Best ResponseYou've already chosen the best response.0but the textbook showed me a differnt answer

mathteacher1729
 5 years ago
Best ResponseYou've already chosen the best response.0Start by dividing everything in the numerator and everything in the denominator by x^3. This gives: \[\lim x \to \infty \frac{\frac{1}{x^3}\sqrt{9x^6x}}{\frac{1}{x^3}(x^3+9)} \] 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: \[\frac{\sqrt{90}}{1}=3\] And that's your answer. Wooo.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0better not have showed a different answer. maybe a different method, but not a different answer.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0mathteacher wrote out all the details, but if i was doing it on an exam i would use my eyes

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok i will continut to show my professor this step to see if i can get credits thanks

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0good idea. that is the "proof" so write that out.
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