Question

Show sequence eventually strictly increases or eventually strictly decreases. {n/ ln(n)} +infinity, n=2

Answer 1

Can you draw it as is in the question?
Use the "draw button".

Answer 2

\[\left\{ \frac{ x }{ \ln x } \right\} ^{+\infty}_{n=2}\]

Answer 3

Using n's in the equation instead of x's. Sorry.

Asked to show that sequence is eventually increasing or eventually decreasing and determine smallest value of n

Answer 4

Smallest value of n such that what?

Answer 5

Determine smallest value of n for which the sequence is eventually strictly increasing or decreasing.

Answer 6

Here's the graph. All you need is the point where n/ln begins to exist definitely.
https://www.google.com/search?q=n%2F+ln(n&rlz=1C1CHFX_enUS524US524&oq=n%2F+ln(n&aqs=chrome.0.69i57j69i58j69i64l2&sourceid=chrome&ie=UTF-8#safe=off&rlz=1C1CHFX_enUS524US524&q=x/ln+x&spell=1&sa=X&psj=1&ei=bWnvUdajEYzy8ASp1IGADQ&ved=0CCoQBSgA&bav=on.2,or.r_qf.&bvm=bv.49641647%2Cd.eWU%2Cpv.xjs.s.en_US.NyLNrjc7wJY.O&fp=3021d1819c6f28ea&biw=1438&bih=839

Answer 7

Which is where ln(n) = 0, therefore at n = 1.

Answer 8

Do you know how to calculate using to derivative rule?

Answer 9

Yeah.

Answer 10

Let's use x instead of n.

Answer 11

Ignore my previous answer. The graph starts from 2 , so 1 is not included.

Answer 12

I've gotten to \[\frac{ \ln (x) - 1 }{ (\ln (x))^{2}}\] now what do I do?

Answer 13

From that, you get x = e^1 = e

Answer 14

How do I find the smallest value of n from e?

Answer 15

I think you should create a new question and make your prompt clearer. The smallest value is -infinity, but it looks like you're needing another type of answer.
Try to create a new question and put more info. This one is already convoluted.