Math

Mathematical Applications for the Management, Life, and Social SciencesIn each of Problems 5 and 6, one of parts (a) and (b) can be integrated with the Power Rule and the other cannot. Integrate the part that can be done with the Power Rule, and explain why the Power Rule cannot be used to evaluate the other. (a) ∫ ( 3 x 4 − 7 ) 12 ( 12 x d x ) (b) ∫ ( 5 x 3 + 11 ) 7 ( 15 x 2 d x )BuyFind*launch*

11th Edition

Ronald J. Harshbarger + 1 other

Publisher: Cengage Learning

ISBN: 9781305108042

Chapter 12.2, Problem 3E

Textbook Problem

In each of Problems 5 and 6, one of parts (a) and (b) can be integrated with the Power Rule and the other cannot. Integrate the part that can be done with the Power Rule, and explain why the Power Rule cannot be used to evaluate the other.

(a)

(b)

Mathematical Applications for the Management, Life, and Social Sciences

Ch. 12.1 - 1. True or false:
(a)
(b)
Ch. 12.1 - 2. Evaluate
Ch. 12.1 - 1. If what is
Ch. 12.1 - 2. If what is
Ch. 12.1 - 3. If what is
Ch. 12.1 - 4. If what is
Ch. 12.1 - Evaluate the integrals in Problems 5-28. Check...Ch. 12.1 - Evaluate the integrals in Problems 5-28. Check...Ch. 12.1 - Evaluate the integrals in Problems 5-28. Check...Ch. 12.1 - Evaluate the integrals in Problems 5-28. Check...

Ch. 12.1 - Evaluate the integrals in Problems 5-28. Check...Ch. 12.1 - Evaluate the integrals in Problems 5-28. Check...Ch. 12.1 - Evaluate the integrals in Problems 5-28. Check...Ch. 12.1 - Evaluate the integrals in Problems 5-28. Check...Ch. 12.1 - Evaluate the integrals in Problems 5-28. Check...Ch. 12.1 - Evaluate the integrals in Problems 5-28. Check...Ch. 12.1 - Evaluate the integrals in Problems 5-28. Check...Ch. 12.1 - Evaluate the integrals in Problems 5-28. Check...Ch. 12.1 - Evaluate the integrals in Problems 5-28. Check...Ch. 12.1 - Evaluate the integrals in Problems 5-28. Check...Ch. 12.1 - Evaluate the integrals in Problems 5-28. Check...Ch. 12.1 - Evaluate the integrals in Problems 5-28. Check...Ch. 12.1 - Evaluate the integrals in Problems 5-28. Check...Ch. 12.1 - Evaluate the integrals in Problems 5-28. Check...Ch. 12.1 - Evaluate the integrals in Problems 5-28. Check...Ch. 12.1 - Evaluate the integrals in Problems 5-28. Check...Ch. 12.1 - Evaluate the integrals in Problems 5-28. Check...Ch. 12.1 - Evaluate the integrals in Problems 5-28. Check...Ch. 12.1 - Evaluate the integrals in Problems 5-28. Check...Ch. 12.1 - Evaluate the integrals in Problems 5-28. Check...Ch. 12.1 - In Problems 29-32, use algebra to rewrite the...Ch. 12.1 - In Problems 29-32, use algebra to rewrite the...Ch. 12.1 - In Problems 29-32, use algebra to rewrite the...Ch. 12.1 - In Problems 29-32, use algebra to rewrite the...Ch. 12.1 - In Problems 33 and 34, find the antiderivatives...Ch. 12.1 - In Problems 33 and 34, find the antiderivatives...Ch. 12.1 - 35. If , find .
Ch. 12.1 - 36. If , find .
Ch. 12.1 - In each of Problems 37-40, a family of functions...Ch. 12.1 - In each of Problems 37-40, a family of functions...Ch. 12.1 - In each of Problems 37-40, a family of functions...Ch. 12.1 - In each of Problems 37-40, a family of functions...Ch. 12.1 - 41. Revenue If the marginal revenue (in dollars...Ch. 12.1 - 42. Revenue If the marginal revenue (in dollars...Ch. 12.1 - 43. Revenue If the marginal revenue (in dollars...Ch. 12.1 - 44. Revenue If the marginal revenue (in dollars...Ch. 12.1 - 45. Stimulus-response Suppose that when a sense...Ch. 12.1 - 46. Projectiles Suppose that a particle has been...Ch. 12.1 - 47. Pollution A factory is damping pollutants into...Ch. 12.1 - 48. Population growth The rate of growth of the...Ch. 12.1 - 49. Average cost The DeWitt Company has found that...Ch. 12.1 - 50. Oil leakage An oil tanker hits a reef and...Ch. 12.1 - Health expenditures per capita National health...Ch. 12.1 - 52. Total taxable payroll By using Social Security...Ch. 12.1 - 53. Wind chill When the air temperature is , the...Ch. 12.1 - 54. Severe weather ice makers Hail is produced in...Ch. 12.1 - 55. U.S. population With U.S. Census Bureau data...Ch. 12.1 - 56. Consumer prices The consumer price index (CPI)...Ch. 12.2 - 1. Which of the following can be evaluated with...Ch. 12.2 - 2. Which of the following is equal to ?
(a)
(b)...Ch. 12.2 - 3. True or false: Constants can be factored...Ch. 12.2 - 4. Evaluate the following.
(a)
(b)
(c)
Ch. 12.2 - In Problems 1-4, find the differential of each...Ch. 12.2 - In Problems 1-4, find the differential of each...Ch. 12.2 - In each of Problems 5 and 6, one of parts (a) and...Ch. 12.2 - In each of Problems 5 and 6, one of parts (a) and...Ch. 12.2 - Evaluate the integrals in Problems 7-36. Check...Ch. 12.2 - Evaluate the integrals in Problems 7-36. Check...Ch. 12.2 - Evaluate the integrals in Problems 7-36. Check...Ch. 12.2 - Evaluate the integrals in Problems 7-36. Check...Ch. 12.2 - Evaluate the integrals in Problems 7-36. Check...Ch. 12.2 - Evaluate the integrals in Problems 7-36. Check...Ch. 12.2 - Evaluate the integrals in Problems 7-36. Check...Ch. 12.2 - Evaluate the integrals in Problems 7-36. Check...Ch. 12.2 - Evaluate the integrals in Problems 7-36. Check...Ch. 12.2 - Evaluate the integrals in Problems 7-36. Check...Ch. 12.2 - Evaluate the integrals in Problems 7-36. Check...Ch. 12.2 - Evaluate the integrals in Problems 7-36. Check...Ch. 12.2 - Evaluate the integrals in Problems 7-36. Check...Ch. 12.2 - Evaluate the integrals in Problems 7-36. Check...Ch. 12.2 - Evaluate the integrals in Problems 7-36. Check...Ch. 12.2 - Evaluate the integrals in Problems 7-36. Check...Ch. 12.2 - Evaluate the integrals in Problems 7-36. Check...Ch. 12.2 - Evaluate the integrals in Problems 7-36. Check...Ch. 12.2 - Evaluate the integrals in Problems 7-36. Check...Ch. 12.2 - Evaluate the integrals in Problems 7-36. Check...Ch. 12.2 - Evaluate the integrals in Problems 7-36. Check...Ch. 12.2 - Evaluate the integrals in Problems 7-36. Check...Ch. 12.2 - Evaluate the integrals in Problems 7-36. Check...Ch. 12.2 - Evaluate the integrals in Problems 7-36. Check...Ch. 12.2 - Evaluate the integrals in Problems 7-36. Check...Ch. 12.2 - Evaluate the integrals in Problems 7-36. Check...Ch. 12.2 - Evaluate the integrals in Problems 7-36. Check...Ch. 12.2 - Evaluate the integrals in Problems 7-36. Check...Ch. 12.2 - Evaluate the integrals in Problems 7-36. Check...Ch. 12.2 - Evaluate the integrals in Problems 7-36. Check...Ch. 12.2 - 37. If find
Ch. 12.2 - 38. If find
Ch. 12.2 - In Problems 39 and 40, (a) evaluate each integral...Ch. 12.2 - In Problems 39 and 40, (a) evaluate each integral...Ch. 12.2 - Each of Problems 41 and 42 has the form dx.
(a)...Ch. 12.2 - Each of Problems 41 and 42 has the form dx.
(a)...Ch. 12.2 - In each of Problems 43 and 44, a family of...Ch. 12.2 - In each of Problems 43 and 44, a family of...Ch. 12.2 - In parts (a)-(c) of Problems 45 and 46, three...Ch. 12.2 - In parts (a)-(c) of Problems 45 and 46, three...Ch. 12.2 - 47. Revenue Suppose that the marginal revenue for...Ch. 12.2 - 48. Revenue The marginal revenue for a new...Ch. 12.2 - 49. Physical productivity The total physical...Ch. 12.2 - 50. Production The rate of production of a new...Ch. 12.2 - 51. Data entry speed The rate of change in data...Ch. 12.2 - 52. Productivity Because a new employee must learn...Ch. 12.2 - 53. Film attendance An excellent film with a very...Ch. 12.2 - 54. Product quality and advertising An inferior...Ch. 12.2 - 55. Demographics Because of job outsourcing, a...Ch. 12.2 - 56. Franchise growth A new fast-food firm predicts...Ch. 12.3 - 1. True or false:
(a) (b)
(c) (d)
Ch. 12.3 - 2. True or false:
(a) (b)
(c) (d)
(e) To...Ch. 12.3 - 3. (a) Divide into 4x.
(b) Evaluate .
Ch. 12.3 - Evaluate the integrals in Problems 1-32.
Ch. 12.3 - Evaluate the integrals in Problems 1-32.
2.
Ch. 12.3 - Evaluate the integrals in Problems 1-32.
3.
Ch. 12.3 - Evaluate the integrals in Problems 1-32.
4.
Ch. 12.3 - Evaluate the integrals in Problems 1-32.
Ch. 12.3 - Evaluate the integrals in Problems 1-32.
Ch. 12.3 - Evaluate the integrals in Problems 1-32.
Ch. 12.3 - Evaluate the integrals in Problems 1-32.
Ch. 12.3 - Evaluate the integrals in Problems 1-32.
9.
Ch. 12.3 - Evaluate the integrals in Problems 1-32.
10.
Ch. 12.3 - Evaluate the integrals in Problems 1-32.
Ch. 12.3 - Evaluate the integrals in Problems 1-32.
12.
Ch. 12.3 - Evaluate the integrals in Problems 1-32.
13.
Ch. 12.3 - Evaluate the integrals in Problems 1-32.
14.
Ch. 12.3 - Evaluate the integrals in Problems 1-32.
15.
Ch. 12.3 - Evaluate the integrals in Problems 1-32.
16.
Ch. 12.3 - Evaluate the integrals in Problems 1-32.
17.
Ch. 12.3 - Evaluate the integrals in Problems 1-32.
18.
Ch. 12.3 - Evaluate the integrals in Problems 1-32.
19.
Ch. 12.3 - Evaluate the integrals in Problems 1-32.
20.
Ch. 12.3 - Evaluate the integrals in Problems 1-32.
21.
Ch. 12.3 - Evaluate the integrals in Problems 1-32.
22.
Ch. 12.3 - Evaluate the integrals in Problems 1-32.
23.
Ch. 12.3 - Evaluate the integrals in Problems 1-32.
24.
Ch. 12.3 - Evaluate the integrals in Problems 1-32.
25.
Ch. 12.3 - Evaluate the integrals in Problems 1-32.
26
Ch. 12.3 - Evaluate the integrals in Problems 1-32.
27.
Ch. 12.3 - Evaluate the integrals in Problems 1-32.
28.
Ch. 12.3 - Evaluate the integrals in Problems 1-32.
29.
Ch. 12.3 - Evaluate the integrals in Problems 1-32.
30.
Ch. 12.3 - Evaluate the integrals in Problems 1-32.
31.
Ch. 12.3 - Evaluate the integrals in Problems 1-32.
32.
Ch. 12.3 - In Problems 33 and 34, graphs of two functions...Ch. 12.3 -
In Problems 33 and 34, graphs of two functions...Ch. 12.3 - In Problems 35 and 36, a function and its graph...Ch. 12.3 - In Problems 35 and 36, a function and its graph...Ch. 12.3 - In Problems 37-40, a family of functions is given...Ch. 12.3 - In Problems 37-40, a family of functions is given...Ch. 12.3 - In Problems 37-40, a family of functions is given...Ch. 12.3 - In Problems 37-40, a family of functions is given...Ch. 12.3 - In parts (a)-(d) of Problems 41 and 42, integrate...Ch. 12.3 - In parts (a)-(d) of Problems 41 and 42, integrate...Ch. 12.3 - 43. Revenue Suppose that the marginal revenue from...Ch. 12.3 - 44. Concentration of a drug Suppose that the rate...Ch. 12.3 - 45. Radioactive decay The rate of disintegration...Ch. 12.3 - 46. Radioactive decay Radioactive substances decay...Ch. 12.3 - 47. Memorization The rate of vocabulary...Ch. 12.3 - 48. Population growth The rate of growth of world...Ch. 12.3 - 49. Compound interest If $P is invested for n...Ch. 12.3 - 50. Temperature changes When an object is moved...Ch. 12.3 - 56. Average annual wage The following table shows...Ch. 12.4 - 1. True or false:
(a) If , then the constant of...Ch. 12.4 - 2. Find and fixed costs are $8000.
Ch. 12.4 - 3. If the marginal propensity to save is
find the...Ch. 12.4 - 4. Find the national consumption function if the...Ch. 12.4 - In Problems 1-12, cost, revenue, and profit are in...Ch. 12.4 - In Problems 1-12, cost, revenue, and profit are in...Ch. 12.4 - In Problems 1-12, cost, revenue, and profit are in...Ch. 12.4 - TOTAL COST AND PROFIT In Problems 1-12, cost,...Ch. 12.4 - TOTAL COST AND PROFIT In Problems 1-12, cost,...Ch. 12.4 - TOTAL COST AND PROFIT In Problems 1-12, cost,...Ch. 12.4 - In Problems 1-12, cost, revenue, and profit are in...Ch. 12.4 - In Problems 1-12, cost, revenue, and profit are in...Ch. 12.4 - In Problems 1-12, cost, revenue, and profit are in...Ch. 12.4 - In Problems 1-12, cost, revenue, and profit are in...Ch. 12.4 - In Problems 1-12, cost, revenue, and profit are in...Ch. 12.4 - In Problems 1-12, cost, revenue, and profit are in...Ch. 12.4 - 14. Suppose that the marginal cost for a certain...Ch. 12.4 - 14. Suppose that the marginal cost for a certain...Ch. 12.4 - If consumption is $7 trillion when disposable...Ch. 12.4 - If national consumption is $9 trillion when income...Ch. 12.4 - If consumption is $8 trillion when income is $0...Ch. 12.4 - If consumption is $5 trillion when disposable...Ch. 12.4 - If consumption is $6 trillion when disposable...Ch. 12.4 - If consumption is $5.8 trillion when disposable...Ch. 12.4 - Suppose that the marginal propensity to consume is...Ch. 12.4 - Suppose that the marginal propensity to save is...Ch. 12.4 - Suppose that the marginal propensity to save is...Ch. 12.4 - If consumption is $3 trillion when disposable...Ch. 12.5 - 1. Given ,
(a) find the general solution to the...Ch. 12.5 - 2. True or false:
(a) The general solution to can...Ch. 12.5 - 3. Suppose that .
(a) Separate this equation. (b)...Ch. 12.5 - In Problems 1-4, show that the given function is a...Ch. 12.5 - In Problems 1-4, show that the given function is a...Ch. 12.5 - In Problems 1-4, show that the given function is a...Ch. 12.5 - In Problems 1-4, show that the given function is a...Ch. 12.5 - In Problems 5-10, use integration to find the...Ch. 12.5 - In Problems 5-10, use integration to find the...Ch. 12.5 - In Problems 5-10, use integration to find the...Ch. 12.5 - In Problems 5-10, use integration to find the...Ch. 12.5 - In Problems 5-10, use integration to find the...Ch. 12.5 - In Problems 5-10, use integration to find the...Ch. 12.5 - In Problems 11-14, find the particular solution.
Ch. 12.5 - In Problems 11-14, find the particular solution.
Ch. 12.5 - In Problems 11-14, find the particular solution.
Ch. 12.5 - In Problems 11-14, find the particular solution.
Ch. 12.5 - In Problems 15-28, find the general solution to...Ch. 12.5 - In Problems 15-28, find the general solution to...Ch. 12.5 - In Problems 15-28, find the general solution to...Ch. 12.5 - In Problems 15-28, find the general solution to...Ch. 12.5 - In Problems 15-28, find the general solution to...Ch. 12.5 - In Problems 15-28, find the general solution to...Ch. 12.5 - In Problems 15-28, find the general solution to...Ch. 12.5 - In Problems 15-28, find the general solution to...Ch. 12.5 - In Problems 15-28, find the general solution to...Ch. 12.5 - In Problems 15-28, find the general solution to...Ch. 12.5 - In Problems 15-28, find the general solution to...Ch. 12.5 - In Problems 15-28, find the general solution to...Ch. 12.5 - In Problems 15-28, find the general solution to...Ch. 12.5 - In Problems 15-28, find the general solution to...Ch. 12.5 - In Problems 29-36, find the particular solution to...Ch. 12.5 - In Problems 29-36, find the particular solution to...Ch. 12.5 - In Problems 29-36, find the particular solution to...Ch. 12.5 - In Problems 29-36, find the particular solution to...Ch. 12.5 - In Problems 29-36, find the particular solution to...Ch. 12.5 - In Problems 29-36, find the particular solution to...Ch. 12.5 - In Problems 29-36, find the particular solution to...Ch. 12.5 - In Problems 29-36, find the particular solution to...Ch. 12.5 - 37. Allometric growth If x and y are measurements...Ch. 12.5 - 38. Bimolecular chemical reactions A bimolecular...Ch. 12.5 - Compound interest In Problems 39 and 40, use the...Ch. 12.5 - Compound interest In Problems 39 and 40, use the...Ch. 12.5 - 41. Investing When the interest on an investment...Ch. 12.5 - 42. Investing When the interest on an investment...Ch. 12.5 - 43. Bacterial growth Suppose that the growth of a...Ch. 12.5 - 44. Bacterial growth Suppose that for a certain...Ch. 12.5 - 46. Sales and pricing Suppose that a chain of auto...Ch. 12.5 - 46. Sales and pricing Suppose that a chain of auto...Ch. 12.5 - 47. Half-life A breeder reactor converts...Ch. 12.5 - 48. Radioactive decay A certain radioactive...Ch. 12.5 - 49. Drug in an organ Suppose that a liquid carries...Ch. 12.5 - 50. Drug in an organ Suppose that a liquid carries...Ch. 12.5 - 51. Drug in an organ Suppose that a liquid carries...Ch. 12.5 - 52. Drug in an organ Suppose that a liquid carries...Ch. 12.5 - 53. Tumor volume Let V denote the volume of a...Ch. 12.5 - 54. Gompertz curves The differential...Ch. 12.5 - 55. Cell growth If V is the volume of a spherical...Ch. 12.5 - 56. Atmospheric pressure The rate of change of...Ch. 12.5 - 57. Newton's law of cooling Newton’s law of...Ch. 12.5 - 58. Newton’s law of cooling Newton’s law of...Ch. 12 - Evaluate the integrals in Problems 1-26.
Ch. 12 - Evaluate the integrals in Problems 1-26.
Ch. 12 - Evaluate the integrals in Problems 1-26.
Ch. 12 - Evaluate the integrals in Problems 1-26.
Ch. 12 - Evaluate the integrals in Problems 1-26.
Ch. 12 - Evaluate the integrals in Problems 1-26.
Ch. 12 - Evaluate the integrals in Problems 1-26.
Ch. 12 - Evaluate the integrals in Problems 1-26.
Ch. 12 - Evaluate the integrals in Problems 1-26.
9.
Ch. 12 - Evaluate the integrals in Problems 1-26.
10.
Ch. 12 - Evaluate the integrals in Problems 1-26.
11.
Ch. 12 - Evaluate the integrals in Problems 1-26.
12.
Ch. 12 - Evaluate the integrals in Problems 1-26.
13.
Ch. 12 - Evaluate the integrals in Problems 1-26.
14.
Ch. 12 - Evaluate the integrals in Problems 1-26.
15.
Ch. 12 - Evaluate the integrals in Problems 1-26.
Ch. 12 - Evaluate the integrals in Problems 1-26.
Ch. 12 - Evaluate the integrals in Problems 1-26.
Ch. 12 - Evaluate the integrals in Problems 1-26.
Ch. 12 - Evaluate the integrals in Problems 1-26.
Ch. 12 - Evaluate the integrals in Problems 1-26.
Ch. 12 - Evaluate the integrals in Problems 1-26.
Ch. 12 - Evaluate the integrals in Problems 1-26.
Ch. 12 - Evaluate the integrals in Problems 1-26.
Ch. 12 - Evaluate the integrals in Problems 1-26.
25. (a) ...Ch. 12 - Evaluate the integrals in Problems 1-26.
26. (a) ...Ch. 12 - In Problems 27-32, find the general solution to...Ch. 12 - In Problems 27-32, find the general solution to...Ch. 12 - In Problems 27-32, find the general solution to...Ch. 12 - In Problems 27-32, find the general solution to...Ch. 12 - In Problems 27-32, find the general solution to...Ch. 12 - In Problems 27-32, find the general solution to...Ch. 12 - In Problems 33 and 34, find the particular...Ch. 12 - In Problems 33 and 34, find the particular...Ch. 12 - 35. Revenue If the marginal revenue for a month...Ch. 12 - 36. Productivity Suppose that the rate of change...Ch. 12 - 37. Oxygen levels in water The rate of change of...Ch. 12 - 38. Bacterial growth A population of bacteria...Ch. 12 - 39. Market share The rate of change of the market...Ch. 12 - 40. Revenue If the marginal revenue for a product...Ch. 12 - 41. Cost The marginal cost for a product is
...Ch. 12 - 42. Profit Suppose a product has a daily marginal...Ch. 12 - National consumption If consumption is $8.5...Ch. 12 - 44. National consumption Suppose that the marginal...Ch. 12 - 45. Allometric growth For many species of fish,...Ch. 12 - 46. Investment When the interest on an investment...Ch. 12 - 47. Fossil dating Radioactive beryllium is...Ch. 12 - 48. Drug in an organ Suppose that a liquid carries...Ch. 12 - 49. Chemical mixture A 300-gal tank initially...Ch. 12 - Evaluate the integrals in Problems 1-11
1.
Ch. 12 - Evaluate the integrals in Problems 1-11.
Ch. 12 - Evaluate the integrals in Problems 1-11.
Ch. 12 - Evaluate the integrals in Problems 1-11.
4.
Ch. 12 - Evaluate the integrals in Problems 1-11.
Ch. 12 - Evaluate the integrals in Problems 1-11.
Ch. 12 - Evaluate the integrals in Problems 1-11.
Ch. 12 - Evaluate the integrals in Problems 1-11.
8.
Ch. 12 - Evaluate the integrals in Problems 1-11.
9.
Ch. 12 - Evaluate the integrals in Problems 1-26.
10.
Ch. 12 - Evaluate the integrals in Problems 1-11.
11.
Ch. 12 - 12. Evaluate Use long division.
Ch. 12 - 13. .
Ch. 12 - 14. Find the general solution to
Ch. 12 - In Problems 15 and 16, find the particular...Ch. 12 - In Problems 15 and 16, find the particular...Ch. 12 - 17. Find the general solution of the separable...Ch. 12 - Suppose the rate of growth of the population of a...Ch. 12 - 19. Suppose that the marginal cost for x units of...Ch. 12 - Suppose the marginal propensity to save is given...Ch. 12 - A certain radioactive material has a half-life of...Ch. 12 - 22. Suppose that a liquid carries a drug with...

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