Calculus with Applications (11th Edition)
11th Edition
ISBN: 9780321979421
Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey
Publisher: PEARSON
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Chapter 9.6, Problem 25E
To determine
To find: The value of
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A small company of science writers found that its rate of profit (in thousands of dollars) after t years of operation is given by P'(t) = (5t + 15) (t² + 6t+9) ³.
(a) Find the total profit in the first three years.
(b) Find the profit in the sixth year of operation.
(c) What is happening to the annual profit over the long run?
(a) The total profit in the first three years is $
(Round to the nearest dollar as needed.)
Find the area between the curves.
x= -2, x = 7, y=2x² +3, y=0
Set up the integral (or integrals) needed to compute this area. Use the smallest possible number
of integrals. Select the correct choice below and fill in the answer boxes to complete your choice.
A.
7
[[2x² +3] dx
-2
B.
[[ ] dx+
-2
7
S [ ] dx
The area between the curves is
(Simplify your answer.)
The rate at which a substance grows is given by R'(x) = 105e0.3x, where x is the time (in days).
What is the total accumulated growth during the first 2.5 days?
Set up the definite integral that determines the accumulated growth during the first 2.5 days.
2.5
Growth = (105e0.3x) dx
0
(Type exact answers in terms of e.)
Evaluate the definite integral.
Growth=
(Do not round until the final answer. Then round to one decimal place as needed.)
Chapter 9 Solutions
Calculus with Applications (11th Edition)
Ch. 9.1 - YOUR TURN 1 For the function in Example 1, find...Ch. 9.1 - YOUR TURN 2 For the function in Example 3, find...Ch. 9.1 - YOUR TURN 3 Graph x + 2y + 3z = 12 in the first...Ch. 9.1 - YOUR TURN 4 Find the level curve at a production...Ch. 9.1 - Prob. 1WECh. 9.1 - Prob. 2WECh. 9.1 - Prob. 3WECh. 9.1 - Prob. 4WECh. 9.1 - Prob. 5WECh. 9.1 - Prob. 6WE
Ch. 9.1 - 1. Let f(x, y) = 2x – 3y + 5. Find the...Ch. 9.1 - 2. Let g(x, y) = x2 – 2xy + y3. Find the...Ch. 9.1 - Prob. 3ECh. 9.1 - 4. Let . Find the following.
(a) f(10,...Ch. 9.1 - Prob. 5ECh. 9.1 - 6. Let f(x, y) = xex+y. Find the...Ch. 9.1 - Prob. 7ECh. 9.1 - Prob. 8ECh. 9.1 - Graph the first-octant portion of each...Ch. 9.1 - Graph the first-octant portion of each...Ch. 9.1 - Prob. 11ECh. 9.1 - Prob. 12ECh. 9.1 - Prob. 13ECh. 9.1 - Prob. 14ECh. 9.1 - Prob. 15ECh. 9.1 - Graph the level curves in the first quadrant of...Ch. 9.1 - Graph the level curves in the first quadrant of...Ch. 9.1 - Graph the level curves in the first quadrant of...Ch. 9.1 - Prob. 19ECh. 9.1 - Prob. 20ECh. 9.1 - Prob. 21ECh. 9.1 - Prob. 22ECh. 9.1 - Match each equation in Exercises 23–28 with its...Ch. 9.1 - Prob. 24ECh. 9.1 - Match each equation in Exercises 23–28 with its...Ch. 9.1 - Prob. 26ECh. 9.1 - Match each equation in Exercises 23–28 with its...Ch. 9.1 - Match each equation in Exercises 23–28 with its...Ch. 9.1 - 29. Let f(x, y) = 4x2 – 2y2, and find the...Ch. 9.1 - Prob. 30ECh. 9.1 - Prob. 31ECh. 9.1 - Prob. 32ECh. 9.1 - 33. Production Production of a digital camera is...Ch. 9.1 - Production Find the level curve at a production of...Ch. 9.1 - Production Find the level curve at a production of...Ch. 9.1 - Prob. 36ECh. 9.1 - 37. Cost If labor (x) costs $250 per unit,...Ch. 9.1 - Prob. 38ECh. 9.1 - Prob. 39ECh. 9.1 - Prob. 40ECh. 9.1 - Prob. 41ECh. 9.1 - 42. Dinosaur Running An article titled “How...Ch. 9.1 - Prob. 43ECh. 9.1 - 44. Dengue Fever In tropical regions, dengue fever...Ch. 9.1 - Prob. 45ECh. 9.1 - Prob. 46ECh. 9.1 - Prob. 47ECh. 9.1 - Prob. 48ECh. 9.1 - Prob. 49ECh. 9.1 - Prob. 50ECh. 9.1 - 51. Elliptical Templates The holes cut in a roof...Ch. 9.2 - YOUR TURN 1 Let Find and .
Ch. 9.2 - Prob. 2YTCh. 9.2 - Prob. 3YTCh. 9.2 - Prob. 4YTCh. 9.2 - Prob. 1WECh. 9.2 - Prob. 2WECh. 9.2 - Prob. 3WECh. 9.2 - Prob. 4WECh. 9.2 - Prob. 5WECh. 9.2 - Prob. 6WECh. 9.2 - Prob. 7WECh. 9.2 - Prob. 8WECh. 9.2 - Prob. 1ECh. 9.2 - Prob. 2ECh. 9.2 - Prob. 3ECh. 9.2 - In Exercises 3–20, find fx(x, y) and fy(x,y). Then...Ch. 9.2 - In Exercises 3–20, find fx(x, y) and fy(x, y)....Ch. 9.2 - Prob. 6ECh. 9.2 - Prob. 7ECh. 9.2 - Prob. 8ECh. 9.2 - Prob. 9ECh. 9.2 - Prob. 10ECh. 9.2 - Prob. 11ECh. 9.2 - Prob. 12ECh. 9.2 - In Exercises 3–20, find fx(x, y) and fy(x, y)....Ch. 9.2 - Prob. 14ECh. 9.2 - Prob. 15ECh. 9.2 - Prob. 16ECh. 9.2 - Prob. 17ECh. 9.2 - Prob. 18ECh. 9.2 - In Exercises 3–20, find fx(x, y) and fy(x, y)....Ch. 9.2 - Prob. 20ECh. 9.2 - Prob. 21ECh. 9.2 - Prob. 22ECh. 9.2 - Prob. 23ECh. 9.2 - Prob. 24ECh. 9.2 - Prob. 25ECh. 9.2 - Prob. 26ECh. 9.2 - Prob. 27ECh. 9.2 - Prob. 28ECh. 9.2 - Prob. 29ECh. 9.2 - Prob. 30ECh. 9.2 - Prob. 31ECh. 9.2 - Prob. 32ECh. 9.2 - Prob. 33ECh. 9.2 - Prob. 34ECh. 9.2 - For the functions defined as follows, find all...Ch. 9.2 - For the functions defined as follows, find all...Ch. 9.2 - Prob. 37ECh. 9.2 - Find and for the following.
38.
Ch. 9.2 - Prob. 39ECh. 9.2 - Prob. 40ECh. 9.2 - Find and for the following.
41.
Ch. 9.2 - Find and for the following.
42.
Ch. 9.2 - Prob. 43ECh. 9.2 - Prob. 44ECh. 9.2 - Business and Economics
45. Manufacturing Cost...Ch. 9.2 - 46. Revenue The revenue from the sale of x units...Ch. 9.2 - Prob. 47ECh. 9.2 - Prob. 48ECh. 9.2 - 49. Marginal Productivity A manufacturer estimates...Ch. 9.2 - 50. Marginal Productivity The production function...Ch. 9.2 - Prob. 51ECh. 9.2 - 52. Marginal Productivity A manufacturer of...Ch. 9.2 - Prob. 53ECh. 9.2 - Prob. 54ECh. 9.2 - Prob. 55ECh. 9.2 - Prob. 56ECh. 9.2 - Prob. 57ECh. 9.2 - Prob. 58ECh. 9.2 - Prob. 59ECh. 9.2 - 60. Health The body mass index (BMI) is a number...Ch. 9.2 - Prob. 61ECh. 9.2 - Prob. 62ECh. 9.2 - 63. Drug Reaction The reaction to x units of a...Ch. 9.2 - Prob. 64ECh. 9.2 - Prob. 66ECh. 9.2 - Prob. 67ECh. 9.2 - Prob. 68ECh. 9.2 - 69. Gravitational Attraction The gravitational...Ch. 9.2 - Prob. 70ECh. 9.2 - Prob. 71ECh. 9.3 - YOUR TURN 1 Find all critical points for
Ch. 9.3 - Prob. 2YTCh. 9.3 - Prob. 1WECh. 9.3 - Prob. 2WECh. 9.3 - Find all points where the functions have any...Ch. 9.3 - Find all points where the functions have any...Ch. 9.3 - Find all points where the functions have any...Ch. 9.3 - Find all points where the functions have any...Ch. 9.3 - Prob. 5ECh. 9.3 - Prob. 6ECh. 9.3 - Prob. 7ECh. 9.3 - Find all points where the functions have any...Ch. 9.3 - Prob. 9ECh. 9.3 - Prob. 10ECh. 9.3 - Prob. 11ECh. 9.3 - Find all points where the functions have any...Ch. 9.3 - Find all points where the functions have any...Ch. 9.3 - Find all points where the functions have any...Ch. 9.3 - Prob. 15ECh. 9.3 - Find all points where the functions have any...Ch. 9.3 - Find all points where the functions have any...Ch. 9.3 - Find all points where the functions have any...Ch. 9.3 - Prob. 19ECh. 9.3 - Prob. 20ECh. 9.3 - Figures (a)–(f) show the graphs of the functions...Ch. 9.3 - Prob. 22ECh. 9.3 - Figures (a)–(f) show the graphs of the functions...Ch. 9.3 - Prob. 24ECh. 9.3 - Prob. 25ECh. 9.3 - Prob. 26ECh. 9.3 - 27. Show that f(x, y) = 1 – x4 – y4 has a relative...Ch. 9.3 - 28. Show that D = 0 for f(x, y) = x3 + (x – y)2...Ch. 9.3 - Prob. 29ECh. 9.3 - Prob. 30ECh. 9.3 - Prob. 31ECh. 9.3 - 32. In Exercise 9 of Section 1.3, we found the...Ch. 9.3 - Prob. 33ECh. 9.3 - 34. Profit Suppose that the profit (in hundreds of...Ch. 9.3 - 35. Labor Costs Suppose the labor cost (in...Ch. 9.3 - 36. Cost The total cost (in dollars) to produce x...Ch. 9.3 - 37. Revenue The total revenue (in hundreds of...Ch. 9.3 - 38. Profit The profit (in thousands of dollars)...Ch. 9.3 - Prob. 39ECh. 9.3 - 40. Political Science The probability that a...Ch. 9.3 - Prob. 42ECh. 9.4 - YOUR TURN 1 Find the minimum value of f(x, y) = x2...Ch. 9.4 - Prob. 1WECh. 9.4 - Prob. 2WECh. 9.4 - Find the relative maxima or minima in Exercises...Ch. 9.4 - Find the relative maxima or minima in Exercises...Ch. 9.4 - Find the relative maxima or minima in Exercises...Ch. 9.4 - Prob. 4ECh. 9.4 - Find the relative maxima or minima in Exercises...Ch. 9.4 - Prob. 6ECh. 9.4 - Find the relative maxima or minima in Exercises...Ch. 9.4 - Prob. 8ECh. 9.4 - Find the relative maxima or minima in Exercises...Ch. 9.4 - Find the relative maxima or minima in Exercises...Ch. 9.4 - 11. Find positive numbers x and y such that x + y...Ch. 9.4 - 12. Find positive numbers x and y such that x + y...Ch. 9.4 - Prob. 13ECh. 9.4 - 14. Find three positive numbers whose sum is 240...Ch. 9.4 - Prob. 15ECh. 9.4 - Prob. 16ECh. 9.4 - Prob. 17ECh. 9.4 - 18. Show that the function f(x, y) = xy2 in...Ch. 9.4 - 19. Show that the function f(x, y) = 8x2y in...Ch. 9.4 - Prob. 20ECh. 9.4 - 21. Consider the problem of minimizing f(x, y) =...Ch. 9.4 - Prob. 22ECh. 9.4 - Business and Economics
Utility Maximize each of...Ch. 9.4 - Business and Economics
Utility Maximize each of...Ch. 9.4 - Business and Economics
Utility Maximize each of...Ch. 9.4 - Prob. 26ECh. 9.4 - 27. Maximum Area for Fixed Expenditure Because of...Ch. 9.4 - 28. Maximum Area for Fixed Expenditure To enclose...Ch. 9.4 - Prob. 29ECh. 9.4 - 30. Profit The profit from the sale of x units of...Ch. 9.4 - 31. Production A manufacturing firm estimates that...Ch. 9.4 - Prob. 32ECh. 9.4 - Prob. 33ECh. 9.4 - Prob. 34ECh. 9.4 - Prob. 35ECh. 9.4 - Prob. 36ECh. 9.4 - Prob. 37ECh. 9.4 - Prob. 38ECh. 9.4 - Prob. 39ECh. 9.4 - Prob. 40ECh. 9.4 - 41. Container Construction RD Enterprises is...Ch. 9.4 - Social Sciences
42. Political Science The...Ch. 9.5 - YOUR TURN 1 For the function , find (a) dz, and...Ch. 9.5 - Prob. 2YTCh. 9.5 - Prob. 3YTCh. 9.5 - Prob. 1WECh. 9.5 - Prob. 2WECh. 9.5 - Prob. 3WECh. 9.5 - Prob. 4WECh. 9.5 - Evaluate dz using the given information.
1.
Ch. 9.5 - Evaluate dz using the given information.
2.
Ch. 9.5 - Evaluate dz using the given information.
3.
Ch. 9.5 - Prob. 4ECh. 9.5 - Evaluate dz using the given information.
5.
Ch. 9.5 - Evaluate dz using the given information.
6.
Ch. 9.5 - Prob. 7ECh. 9.5 - Prob. 8ECh. 9.5 - Use the total differential to approximate each...Ch. 9.5 - Prob. 10ECh. 9.5 - Prob. 11ECh. 9.5 - Prob. 12ECh. 9.5 - Use the total differential to approximate each...Ch. 9.5 - Use the total differential to approximate each...Ch. 9.5 - Prob. 15ECh. 9.5 - Prob. 16ECh. 9.5 - 17. Volume of a Coating An industrial coaling 0.1...Ch. 9.5 - Prob. 18ECh. 9.5 - Prob. 19ECh. 9.5 - Prob. 20ECh. 9.5 - Prob. 21ECh. 9.5 - Prob. 22ECh. 9.5 - 23. Blood Volume In Exercise 58 of Section 2 in...Ch. 9.5 - Prob. 24ECh. 9.5 - Life Span As we saw in Exercise 62 of Section 9.2,...Ch. 9.5 - Prob. 26ECh. 9.5 - Prob. 27ECh. 9.5 - Prob. 28ECh. 9.5 - Prob. 29ECh. 9.5 - Prob. 30ECh. 9.5 - Prob. 31ECh. 9.5 - Prob. 32ECh. 9.5 - Prob. 33ECh. 9.5 - Prob. 34ECh. 9.5 - Prob. 35ECh. 9.6 - YOUR TURN 1 Evaluate
Ch. 9.6 - YOUR TURN 2 Evaluate and then integrate with the...Ch. 9.6 - Prob. 3YTCh. 9.6 - Prob. 4YTCh. 9.6 - Prob. 5YTCh. 9.6 - Prob. 1WECh. 9.6 - Prob. 2WECh. 9.6 - Prob. 3WECh. 9.6 - Prob. 4WECh. 9.6 - Prob. 5WECh. 9.6 - Prob. 6WECh. 9.6 - Prob. 1ECh. 9.6 - Evaluate each integral.
2.
Ch. 9.6 - Prob. 3ECh. 9.6 - Prob. 4ECh. 9.6 - Prob. 5ECh. 9.6 - Evaluate each integral.
6.
Ch. 9.6 - Prob. 7ECh. 9.6 - Prob. 8ECh. 9.6 - Prob. 9ECh. 9.6 - Prob. 10ECh. 9.6 - Evaluate each iterated integral. (Many of these...Ch. 9.6 - Evaluate each iterated integral. (Many of these...Ch. 9.6 - Evaluate each iterated integral. (Many of these...Ch. 9.6 - Prob. 14ECh. 9.6 - Evaluate each iterated integral. (Many of these...Ch. 9.6 - Prob. 16ECh. 9.6 - Evaluate each iterated integral. (Many of these...Ch. 9.6 - Prob. 18ECh. 9.6 - Evaluate each iterated integral. (Many of these...Ch. 9.6 - Evaluate each iterated integral. (Many of these...Ch. 9.6 - Prob. 21ECh. 9.6 - Find each double integral over the rectangular...Ch. 9.6 - Find each double integral over the rectangular...Ch. 9.6 - Prob. 24ECh. 9.6 - Find each double integral over the rectangular...Ch. 9.6 - Find each double integral over the rectangular...Ch. 9.6 - Find each double integral over the rectangular...Ch. 9.6 - Prob. 28ECh. 9.6 - Find the volume under the given surface and above...Ch. 9.6 - Find the volume under the given surface and above...Ch. 9.6 - Prob. 31ECh. 9.6 - Find the volume under the given surface and above...Ch. 9.6 - Find the volume under the given surface and above...Ch. 9.6 - Prob. 34ECh. 9.6 - Find the volume under the given surface and above...Ch. 9.6 - Find the volume under the given surface and above...Ch. 9.6 - Prob. 37ECh. 9.6 - Although it is often true that a double integral...Ch. 9.6 - Prob. 39ECh. 9.6 - Evaluate each double integral.
40.
Ch. 9.6 - Prob. 41ECh. 9.6 - Prob. 42ECh. 9.6 - Prob. 43ECh. 9.6 - Use the region R with the indicated boundaries to...Ch. 9.6 - Prob. 45ECh. 9.6 - Prob. 46ECh. 9.6 - Prob. 47ECh. 9.6 - Use the region R with the indicated boundaries to...Ch. 9.6 - Prob. 49ECh. 9.6 - Prob. 50ECh. 9.6 - Prob. 51ECh. 9.6 - Use the region R with the indicated boundaries to...Ch. 9.6 - Use the region R with the indicated boundaries to...Ch. 9.6 - Use the region R with the indicated boundaries to...Ch. 9.6 - Prob. 55ECh. 9.6 - Prob. 56ECh. 9.6 - Evaluate each double integral. If the function...Ch. 9.6 - Prob. 58ECh. 9.6 - Prob. 59ECh. 9.6 - Prob. 60ECh. 9.6 - The idea of the average value of a function,...Ch. 9.6 - Prob. 62ECh. 9.6 - Prob. 63ECh. 9.6 - Prob. 64ECh. 9.6 - 65. Packaging The manufacturer of a fruit juice...Ch. 9.6 - Prob. 66ECh. 9.6 - 67. Average Production A production function is...Ch. 9.6 - 68. Average Profit The profit (in dollars) from...Ch. 9.6 - 69. Average Revenue A company sells two products....Ch. 9.6 - Prob. 70ECh. 9.6 - Prob. 71ECh. 9 - Prob. 1RECh. 9 - Prob. 2RECh. 9 - Prob. 3RECh. 9 - Prob. 4RECh. 9 - Prob. 5RECh. 9 - Prob. 6RECh. 9 - Prob. 7RECh. 9 - Prob. 8RECh. 9 - Prob. 9RECh. 9 - Prob. 10RECh. 9 - Prob. 11RECh. 9 - Prob. 12RECh. 9 - Prob. 13RECh. 9 - Prob. 14RECh. 9 - Prob. 15RECh. 9 - Prob. 16RECh. 9 - Prob. 17RECh. 9 - Find (–1, 2) and f(6, –3) for the...Ch. 9 - Prob. 19RECh. 9 - Prob. 20RECh. 9 - Prob. 21RECh. 9 - Prob. 22RECh. 9 - Prob. 23RECh. 9 - Prob. 24RECh. 9 - Prob. 25RECh. 9 - Prob. 26RECh. 9 - Prob. 27RECh. 9 - Prob. 28RECh. 9 - Prob. 29RECh. 9 - Prob. 30RECh. 9 - Prob. 31RECh. 9 - Prob. 32RECh. 9 - Prob. 33RECh. 9 - Prob. 34RECh. 9 - Prob. 35RECh. 9 - Prob. 36RECh. 9 - Prob. 37RECh. 9 - Prob. 38RECh. 9 - Prob. 39RECh. 9 - Prob. 40RECh. 9 - Prob. 41RECh. 9 - Prob. 42RECh. 9 - Prob. 43RECh. 9 - Prob. 44RECh. 9 - Prob. 45RECh. 9 - Prob. 46RECh. 9 - Prob. 47RECh. 9 - Prob. 48RECh. 9 - Prob. 49RECh. 9 - Prob. 50RECh. 9 - Prob. 51RECh. 9 - Prob. 52RECh. 9 - Prob. 53RECh. 9 - Prob. 54RECh. 9 - Prob. 55RECh. 9 - Prob. 56RECh. 9 - Prob. 57RECh. 9 - Prob. 58RECh. 9 - Prob. 59RECh. 9 - Prob. 60RECh. 9 - Prob. 61RECh. 9 - Prob. 62RECh. 9 - Prob. 63RECh. 9 - Prob. 64RECh. 9 - Prob. 65RECh. 9 - Prob. 66RECh. 9 - Prob. 67RECh. 9 - Prob. 68RECh. 9 - Prob. 69RECh. 9 - Prob. 70RECh. 9 - Prob. 71RECh. 9 - Prob. 72RECh. 9 - Prob. 73RECh. 9 - Prob. 74RECh. 9 - Prob. 75RECh. 9 - Prob. 76RECh. 9 - Prob. 77RECh. 9 - Prob. 78RECh. 9 - Prob. 79RECh. 9 - Prob. 80RECh. 9 - Prob. 81RECh. 9 - Prob. 82RECh. 9 - Prob. 83RECh. 9 - Prob. 84RECh. 9 - Prob. 85RECh. 9 - Prob. 86RECh. 9 - Prob. 87RECh. 9 - Prob. 88RECh. 9 - Prob. 89RECh. 9 - Prob. 90RECh. 9 - Prob. 91RECh. 9 - Prob. 92RECh. 9 - Prob. 93RECh. 9 - Prob. 94RECh. 9 - Prob. 95RECh. 9 - Prob. 96RECh. 9 - 97. Profit The total profit from 1 acre of a...Ch. 9 - Prob. 98RECh. 9 - Prob. 99RECh. 9 - Prob. 100RECh. 9 - Prob. 101RECh. 9 - Prob. 102RECh. 9 - Prob. 103RECh. 9 - Prob. 104RECh. 9 - Prob. 105RECh. 9 - Prob. 106RE
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