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

geometry: triangles

solvers

lessons

answers archive

call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584

answer:   rotate 270° clockwise about (7, 1) and reflect across the line x = 7

step-by-step explanation:

because i took test