Find the limit of the following sequence or determine that the limit does not exist. {5n/squareroot 81 n^2 + 5} select the correct choice below and, if necessary, fill in the answer box to complete your choice.

a. the sequence is monotonic, but it is unbounded. the limit
b. the sequence is not monotonic, but it is bounded. the limit
c. the sequence is monotonic and bounded. the limit
d. the sequence is monotonic, unbounded, and the limit does not exist.

C. The sequence is monotonic and bounded. The limit is 5/9

Step-by-step explanation:

For this case we have the following n term:

And we can find the limit when x tend to infinity:

And we got this:

Now we can divide by n the numerator and denominator like this:

And now we can apply properties of limits and we got this:

And we got:

So then our sequence is bounded by

By definition a monotonic sequence is a "sequence that is always increasing or decreasing".

For this case if we find:

We see that and in general we see that . So then the ebst answer for this case is:

C. The sequence is monotonic and bounded. The limit is 5/9

step-by-step explanation: