<span>c.)11 over 9, square root of 5, square root of 11, square root of 20, 2 to the power of 3
In order to compare, try to bring all of them into one similar form, like decimal. Then, 11/9 = 1.22 Then, we can compare numbers under root, as 5 would be smaller than 11 which in turn is smaller than the 20, then 2^3 is 8, largest in series.
Let be a sequence that converges to . This means for any , there is some such that for all . From this inequality we see that , so it follows that .
On the other hand, let be a sequence that converges to 0. This means for all large enough , and we get the simpler inequality for free, , so it follows that .