Question

lim x→∞ [(n^2+n)/n^3]=0

Answer 1

What do you need? Check your answer or an explanation on how to get 0?

Answer 2

An explanation please...

Answer 3

Help figuring it out, not an answer.

Answer 4

I have to prove that the limit equals zero.

Answer 5

\[\lim_{n\to \infty}\frac{n^2+1}{n^3}\]
Dividing by the highest power of n in the numerator, you have
\[\large\lim_{n\to \infty}\frac{\frac{n^2+1}{n^2}}{\frac{n^3}{n^2}}=\lim_{n\to \infty}\frac{1+\frac{1}{n^2}}{n}\]
\[\text{As }n\to\infty, \frac{1}{n^2}\to0, \text{ so you have}\\
\lim (\cdots)= \frac{1+0}{\infty}=0\]

Answer 6

Wait, a proof? Like epsilon-delta?

Answer 7

There are no epsilon nor deltas in his study notes, so I don't think so

Answer 8

I guess just "proving" using limit rules, laws, facts??? His course notes are sparse since it is a "review course"

Answer 9

The professor's only hint for the problem set is (You can use the fact lim n→∞ (1/n) = 0)

Answer 10

Oh, well in that case, I hope my explanation was clear enough. I did use that hint/fact towards the end.