I need some help with a question.(adsbygoogle = window.adsbygoogle || []).push({});

Q) Prove that (2n^4 + 4n^2 + 3n - 5)/(n^4 - n^3 + 2n^2 - 80) converges to 2 as n goes to infinity.

A)

By the algebra of limits, this converges to 2 since

lim(n->oo)[2 + 4/n^2 + 3/n^3 - 5/n^4]/lim(n->oo)[1 - 1/n + 2/n^2 - 80/n^4)

(2 + 0 + 0 + 0)/(1 - 0 + 0 + 0) = 2

However, I would like to do this a little more precisely and rigorously. Can someone tell me...

Would I fix epsilon (e) > 0.

Then the absolute value of the quotient minus 2 must be bigger than epsilon, etc...

Or would I approach this in another way.

Any Help woudl be appreciated.

Thanks.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Proof of Least Upper Bound

**Physics Forums | Science Articles, Homework Help, Discussion**