+0  
 
0
264
1
avatar

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
 #1
avatar+26971 
+1

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

20 Online Users

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.