Step-by-step explanation:
arctan(x) is less than π/2 for x > 0. Therefore, if we say g(x) = 13 (π/2) / eˣ, then f(x) < g(x) for all values of x > 0.
g(x) = 13 (π/2) / eˣ
g(x) = 13π/2 · (1/e)ˣ
So g(x) is a geometric series where r = 1/e. Since |r| < 1, the series converges.
Since g(x) converges, the smaller f(x) also converges.
What is your question? that made no sense sweet heart.


- <u>While </u><u>shopping </u><u>for </u><u>clothes </u><u>Tracey </u><u>spent </u><u>3</u><u>8</u><u>$</u><u> </u><u>less </u><u>than </u><u>3</u><u> </u><u>times </u><u>of </u><u>what </u><u>Daniel </u><u>spent </u>

- <u>We </u><u>have </u><u>to </u><u>determine </u><u>the </u><u>total </u><u>cost </u><u>spent </u><u>by </u><u>daniel</u>

Cost spent by Tracey for her clothes = 38$
Let assume the spending by Daniel is x





Answer:
You could just replace all the given possible values of k in the inequality and see which ones are solutions, but let's solve this in a more interesting way:
First, remember how the absolute value works:
IxI = x if x ≥ 0
IxI = -x if x ≤ 0
Then if we have something like:
IxI < B
We can rewrite this as
-B < x < B
Now let's answer the question, here we have the inequality:
I-k -2I < 18
Then we can rewrite this as:
-18 < (-k - 2) < 18
Now let's isolate k:
first, we can add 2 in the 3 parts of the inequality:
-18 + 2 < -k - 2 + 2 < 18 + 2
-16 < -k < 20
Now we can multiply all sides by -1, remember that this also changes the direction of the signs, then:
-1*-16 > -1*-k > -1*20
16 > k > -20
Then k can be any value between these two limits.
So the correct options (from the given ones) are:
k = -16
k = -8
k = 0