I can't seem to find this limit

[Lavender]

Homework Statement

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 :(

 

[haruspex]

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?

 

[Incand]

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.

 

[vela]

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.