anonymous
  • anonymous
evaluate limit ( sqrt(n^2+n) - n )
Calculus1
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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P0sitr0n
  • P0sitr0n
assuming 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
  • anonymous
I have reached to as limit n goes to infinity (n/sqrt(n^2+n) +n)
anonymous
  • anonymous
Dividing by n ?

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P0sitr0n
  • P0sitr0n
ok 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
  • P0sitr0n
yeah, then you cancel both n, and are left with an expression that you can evaluate
anonymous
  • anonymous
Canceling from above ?
anonymous
  • anonymous
Yes I get it now
anonymous
  • anonymous
Thank you

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