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:[tex]\sqrt{3}+5n^2+4n^4[/tex] OR [tex]\sqrt{3+5n^2+4n^4}[/tex] ?
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
[tex]\sqrt{3+5n^2+4n^4}[/tex] / 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
[tex]\sqrt{3+5n^2+4n^4}[/tex] / n^4, or / any number, for that matter. I'm not seeing how to simplify that radical into individual terms.
"n -> infinity" means that the value of n is approaching infinity, or getting infinitely large. This is often used in mathematical notation to indicate that we are looking at the behavior of a function or sequence as its input or index approaches infinity.
To find the limit as n approaches infinity, we evaluate the function or sequence at increasingly large values of n. If the resulting values approach a specific number, that number is the limit. If the values do not approach a specific number, the limit does not exist.
No, the limit as n approaches infinity can only be a specific number if the function or sequence approaches that number as n gets larger and larger. If the function or sequence does not approach a specific number, the limit does not exist.
A finite limit means that the function or sequence approaches a specific number as its input or index approaches a specific value. A limit as n approaches infinity means that the function or sequence approaches a specific number as its input or index gets infinitely large.
Finding the limit as n approaches infinity is important because it helps us understand the behavior of a function or sequence as its input or index gets very large. This can be useful in many areas of mathematics, such as calculus, where we want to understand how functions behave at the edges of their domains.