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Homework Help: What is this expression equal to?

  1. Dec 22, 2016 #1
    • Member reminded to post homework-type questions in the Homework sections
    Basically i need to evaluate the limit of this expression ##\lim \sqrt[3]{n^6-n^4+5}-n^2=?## I want to know if this is correct and why:
    ##\lim \sqrt[3]{n^6-n^4+5}-n^2=\lim \sqrt[3]{n^6-n^4+5}-n^2*\frac{(\sqrt[3]{n^6-n^4+5})^2+n^2\sqrt[3]{n^6-n^4+5}+n^4}{(\sqrt[3]{n^6-n^4+5})^2+n^2\sqrt[3]{n^6-n^4+5}+n^4}=\lim \frac{n^6-n^4+5-n^6}{(\sqrt[3]{n^6-n^4+5})^2+n^2\sqrt[3]{n^6-n^4+5}+n^4}##
    Why does the above fraction equals that? Is that an identity of some kind?
  2. jcsd
  3. Dec 22, 2016 #2


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    Staff: Mentor

    Is this a schoolwork question? If so, I can move it to the Homework Help forums.
  4. Dec 22, 2016 #3


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    Homework Helper

    Do you know the identity:

    ##a^3 - b^3 = (a - b)(a^2 + ab + b^3)##?
  5. Dec 22, 2016 #4


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    Homework Helper

    You meant ##a^3 - b^3 = (a - b)(a^2 + ab + b^2)##.
  6. Dec 23, 2016 #5
    Its not exactly a homework problem but an already finished problem but i didnt understand that part so was looking for the identity. Thanks
  7. Dec 23, 2016 #6


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    Homework Helper

    Ah thanks for correcting the typo.
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