I can't seem to find this limit

  • #1
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Homework Statement


1.jpg

Homework Equations




The Attempt at a Solution


I tried using the rule of multiplying with the "conjugate", for example what's above multiplied by (√n^3+3n)+(√n^3+2n^2+3)/(√n^3+3n)+(√n^3+2n^2+3).
But I'm left with a huge mess :(
I also tried dividing the top and the bottom by n^2 in the square roots to get the n out, but that didn't work either :(
 

Answers and Replies

  • #2
haruspex
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Homework Statement


View attachment 94117

Homework Equations




The Attempt at a Solution


I tried using the rule of multiplying with the "conjugate", for example what's above multiplied by (√n^3+3n)+(√n^3+2n^2+3)/(√n^3+3n)+(√n^3+2n^2+3).
But I'm left with a huge mess :(
I also tried dividing the top and the bottom by n^2 in the square roots to get the n out, but that didn't work either :(
The conjugate method looks good here. It doesn't give a mess in the numerator, right? In the denominator, do you need all the terms, or is it sufficient then only to look at the leading terms?
 
  • #3
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The image is so bad I can't even see the value of the exponents, try to write it out in latex next time.
Assuming what you wrote is ##\frac{\sqrt{n^3+3n}-\sqrt{n^3+2n^2+3}}{\sqrt{n+2}}##
multiplying with the conjugate works for me. After you done that note that only the "highest order" terms matter.
 
  • #4
vela
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I also tried dividing the top and the bottom by n^2 in the square roots to get the n out, but that didn't work either :(
After you multiply by the conjugate, you want to pull the highest power of n, not ##n^2##, out of each of the square roots.
 

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