The discussion revolves around finding the limit of a rational function as n approaches infinity, specifically the expression (n+1)^2 / (√3 + 5n^2 + 4n^4). Participants are exploring the behavior of the function as n increases and the implications of dividing by n^4.
The discussion is active, with participants providing different approaches to simplify the limit expression. Some have offered guidance on how to manipulate the radical and the terms involved, while others are still clarifying their understanding of the setup and simplification process.
There is a noted difficulty in simplifying the radical expression, and participants are working through the implications of dividing by n^4 and how it affects the limit. The original poster indicates uncertainty about the correct form of the denominator, which is crucial for the limit evaluation.
ircdan said:divide the numerator and denominator by n^4
ircdan said:you have, (n+1)^2/(sqrt(3) + 5n^2 + 4n^4), or
(n^2 + 2n + 1)/(sqrt(3) + 5n^2 + 4n^4), so dividing num and denom by n^4,
(1/n^2 + 2/n^3 + 1/n^4)/(sqrt(3)/n^4 + 5/n^2 + 4) and now the limit as n->inf is ...
jdg812 said:\sqrt{3}+5n^2+4n^4 OR \sqrt{3+5n^2+4n^4} ?
if the last one, then divide num and denom by n^2
You should not simplify the radical, just put n^2 INSIDE the radical... and remember that n^2 becomes n^4 when inside radical...dalarev said:It's the last one, everything under the radical.
My problem is I'm not seeing how I would divide something like
\sqrt{3+5n^2+4n^4} / n^4, or / any number, for that matter. I'm not seeing how to simplify that radical into individual terms.
dalarev said:It's the last one, everything under the radical.
My problem is I'm not seeing how I would divide something like
\sqrt{3+5n^2+4n^4} / n^4, or / any number, for that matter. I'm not seeing how to simplify that radical into individual terms.