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Problem with limit

  1. Nov 16, 2011 #1
    Here is my example, could you please check and correct if it needed.
    [itex]\stackrel{lim}{n\rightarrow ∞}\frac{\sqrt{4n^3+1}-\sqrt[3] {n+2}}{\sqrt[3] {n^6+27}+n}=[/itex] [itex]\stackrel{lim}{n\rightarrow ∞}\frac{\sqrt{4n^3}}{n\sqrt[3] {n^6}}=[/itex][itex]\stackrel{lim}{n\rightarrow ∞}{\frac{{{4n}^\frac{3}{2}}}{n^2}}={{4}^\frac{3}{4}}[/itex]
    Thank you!
    Last edited: Nov 16, 2011
  2. jcsd
  3. Nov 16, 2011 #2


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    I don't know how to correct that. Your last two steps, from the limit of [itex]\sqrt{4n^3}/n\sqrt[3]{n^6}[/itex] to the limit of [itex]4n^{3/2}/n^2[/itex] and then to [itex]4^{3/2}[/itex] are pretty much nonsense. Do them again!
  4. Nov 16, 2011 #3
    [itex]\stackrel{lim}{n\rightarrow ∞}\frac{\sqrt{4n^3}}{n\sqrt[3] {n^6}}=[/itex][itex]\stackrel{lim}{n\rightarrow ∞}{\frac{{{n}^\frac{3}{2}}}{n^2}}=\stackrel{lim}{n\rightarrow ∞}{\frac{{1}}{{n}^\frac{1}{2}}}=0[/itex]
    Like this?
  5. Nov 16, 2011 #4


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    Now it looks ok.
  6. Dec 16, 2011 #5
    A little a bit late, but anyway Thanks a lot!
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