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anonymous
 one year ago
evaluate limit ( sqrt(n^2+n)  n )
anonymous
 one year ago
evaluate limit ( sqrt(n^2+n)  n )

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P0sitr0n
 one year ago
Best ResponseYou've already chosen the best response.3assuming we are taking the limit to infinity, simply multiply the top and the bottom by the conjugate of the numerator, i.e. \[(\sqrt{n^2+n}+n)\] Then this will allow you to simplify your fraction up to \[\lim_{n \rightarrow \infty}\frac{n}{\sqrt{n^2+n}+n}\] Now factor and simplify

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I have reached to as limit n goes to infinity (n/sqrt(n^2+n) +n)

P0sitr0n
 one year ago
Best ResponseYou've already chosen the best response.3ok good. Now what you can do is factor out the n^2 out of the square root, which will give you \[n(\sqrt{1+\frac{1}{n}}+1)\] in the bottom

P0sitr0n
 one year ago
Best ResponseYou've already chosen the best response.3yeah, then you cancel both n, and are left with an expression that you can evaluate

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Canceling from above ?
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