- #1

doktorwho

- 181

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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?

##\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?