Question

Determine whether the sequence is increasing, decreasing, or not monotonic.

Answer 1

Okay plz post the problem

Answer 2

\[a_n = \frac{ 7n-8 }{ 8n +3 }\]

Answer 3

don't be confused the "sequence" part of this
imagine you were graphing
\[f(x)=\frac{7x-8}{8x+3}\] would it be increasing, decreasing or neither on \(0,\infty\)?

Answer 4

if it is not clear, you can take the derivative and check

Answer 5

I know that the denom is increasing, and that could mean the seq is decreasing but the numerator throws me off

Answer 6

what is the derivative ?
what does the rational function look like?

Answer 7

MAXIMUM AND MINIMUM
VALUES is that what u are learning

Answer 8

no

Answer 9

no not at all
it is asking if it is increasing or decreasing or neither

Answer 10

did you find the derivative yet?

Answer 11

I did not take that approach, no. I was trying to see if the numerator was also increasing. and if they both are increasing, does that mean that the seq is increasing

Answer 12

no

Answer 13

just because they are both increasing doesn't mean the terms are
for example x and x^2 + 1 are both increasing, but \(\frac{x}{x^2+1}\) would be decreasing on \((0,\infty)\)

Answer 14

are you reluctant to take the derivative? if so, why?

Answer 15

ok...i can see that when put that way!

Answer 16

it just did not cross my mind. this professor does not teach, he just posts hw and says good luck

Answer 17

let me know what you get

Answer 18

or 7/8

Answer 19

hmm forgot the quotient rule already
that is the limit, not the derivative

Answer 20

Determine the first derivative. If it is positive, then the function is increasing. If it is negative, the function is decreasing. The quotient rule for differentiating is

Answer 21

\[\frac{ 85 }{ 64x^2+48x+9 }\]

Answer 22

If\[f(x) = \frac{ g(x) }{ h(x) } \text{ then}\]\[f^\prime (x) = \frac{ g^\prime (x) h(x) - g(x) h^\prime (x) }{ (h(x))^2 }\]

Answer 23

ok. thank you

Answer 24

so, the answer is increasing and bounded

Answer 25

yes it is

Answer 26

the denominator is a square, and the numerator is positive do the derivative is positive
that makes the terms monotone increasing, and the limit is \(\frac{7}{8}\)