Answer:
(a)
(b)P'(5)=-($4.54) Thousand
(c)P'(11)=-($2.10) Thousand
(d)The fifth Month
Step-by-step explanation:
Given the monthly profit model:
(a)We want to derive a model that gives the Marginal Profit, P' of the book.
We differentiate
using quotient rule.
Simplifying
We have derived a model for the marginal profit.
(b) After 5 months, at t=5
Marginal Profit=P'(5)
=-($4.54) Thousand of dollars
(c)Marginal Profit 11 Months after book release
=-($2.10) Thousand of dollars
(d) Since the marginal profit at t=5 is negative, after the 5th Month, the profit starts to experience a steady decrease.
Is there a problem or something to show for it?
Answer: $5.54
Step-by-step explanation: 63 divided by 100 is 0.63, 0.63 x 8.8 is 5.544 and 5.544 rounded to the nearest cent is $5.54
Answer:
∑ (-1)ⁿ⁺³ 1 / (n^½)
∑ (-1)³ⁿ 1 / (8 + n)
Step-by-step explanation:
If ∑ an is convergent and ∑│an│is divergent, then the series is conditionally convergent.
Option A: (-1)²ⁿ is always +1. So an =│an│and both series converge (absolutely convergent).
Option B: bn = 1 / (n^⁹/₈) is a p series with p > 1, so both an and │an│converge (absolutely convergent).
Option C: an = 1 / n³ isn't an alternating series. So an =│an│and both series converge (p series with p > 1). This is absolutely convergent.
Option D: bn = 1 / (n^½) is a p series with p = ½, so this is a diverging series. Since lim(n→∞) bn = 0, and bn is decreasing, then an converges. So this is conditionally convergent.
Option E: (-1)³ⁿ = (-1)²ⁿ (-1)ⁿ = (-1)ⁿ, so this is an alternating series. bn = 1 / (8 + n), which diverges. Since lim(n→∞) bn = 0, and bn is decreasing, then an converges. So this is conditionally convergent.
