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How do i find the limit of this equation: (sqrt(n^3+7n^2)-sqrt(n^3))/(sqrt(n)) when it goes toward infinite

Guest Sep 17, 2017
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Like so:

 

\((\sqrt{n^3+7n^2}-\sqrt{n^3})/\sqrt n \rightarrow \sqrt{n^2+7n}-\sqrt{n^2}\\ \rightarrow (n^2+7n)^{1/2}-n \rightarrow n(1+7/n)^{1/2}-n \\ \rightarrow n(1+(1/2)(7/n)+(1/2)(-1/2)(1/2!)(7/n)^2+...)-n\\ \rightarrow n + 7/2 - 49/(8n) + ... - n \rightarrow 7/2 - 49/(8n) + ...\)

As all the higher order terms involve a power of n in the denominator, they go to zero as n goes to infinity, so we are left with just 7/2 as the limit.

Alan  Sep 17, 2017
edited by Alan  Sep 17, 2017
edited by Alan  Sep 17, 2017

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