Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)
14th Edition
ISBN: 9780134668574
Author: Raymond A. Barnett, Michael R. Ziegler, Karl E. Byleen, Christopher J. Stocker
Publisher: PEARSON
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Textbook Question
Chapter 3.2, Problem 55E
In Problems 47–58, find
55. y = 3 ln x + 2 log3 x
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1. log,x = -2
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In Problems 61–74, use a graphing utility to solve each equation. Express your answer rounded to two decimal places.
61. logs(x + 1) – log4(x – 2) = 1
62. log2 (x – 1) – log6(x + 2) = 2
63. e* = -x
64. e2* = x + 2
65. e* = x²
66. e* = x
69. In x = x – 1
73. e* = In x
67. In x = -x
68. In (2x) = -x + 2
70. In x = -x?
71. e + In x = 4
72. e - In xr = 4
74. e = -In x
Need help with only #51, #52, and #54. I having hard time with those and Thank Your for your help.
Chapter 3 Solutions
Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)
Ch. 3.1 - Matched Problem 1 What amount (to the nearest...Ch. 3.1 - Matched Problem 2 If 5,000 is invested in a Union...Ch. 3.1 - Matched Problem 3 How long will it take an...Ch. 3.1 - Matched Problem 4 How long will it take money to...Ch. 3.1 - Explore and Discuss 1 You are considering three...Ch. 3.1 - In Problems 18, solve for the variable to two...Ch. 3.1 - In Problems 18, solve for the variable to two...Ch. 3.1 - In Problems 18, solve for the variable to two...Ch. 3.1 - In Problems 18, solve for the variable to two...Ch. 3.1 - In Problems 18, solve for the variable to two...
Ch. 3.1 - In Problems 18, solve for the variable to two...Ch. 3.1 - In Problems 18, solve for the variable to two...Ch. 3.1 - In Problems 18, solve for the variable to two...Ch. 3.1 - Use a calculator to evaluate A to the nearest cent...Ch. 3.1 - Use a calculator to evaluate A to the nearest cent...Ch. 3.1 - If 6,000 is invested at 10% compounded...Ch. 3.1 - If 4,000 is invested at 8% compounded...Ch. 3.1 - In Problems 1320, solve for t or r to two decimal...Ch. 3.1 - In Problems 1320, solve for t or r to two decimal...Ch. 3.1 - In Problems 1320, solve for t or r to two decimal...Ch. 3.1 - In Problems 1320, solve for t or r to two decimal...Ch. 3.1 - In Problems 1320, solve for t or r to two decimal...Ch. 3.1 - In Problems 1320, solve for t or r to two decimal...Ch. 3.1 - In Problems 1320, solve for t or r to two decimal...Ch. 3.1 - In Problems 1320, solve for t or r to two decimal...Ch. 3.1 - In Problems 21 and 22, use a calculator to...Ch. 3.1 - In Problems 21 and 22, use a calculator to...Ch. 3.1 - Use a calculator and a table of values to...Ch. 3.1 - Use a calculator and a table of values to...Ch. 3.1 - It can be shown that the number e satisfies the...Ch. 3.1 - It can be shown that es=limn(1+sn)n for any real...Ch. 3.1 - Continuous compound interest. Provident Bank...Ch. 3.1 - Continuous compound interest. Provident Bank also...Ch. 3.1 - Present value. A note will pay 20,000 at maturity...Ch. 3.1 - Present value. A note will pay 50,000 at maturity...Ch. 3.1 - Continuous compound interest. An investor bought...Ch. 3.1 - Continuous compound interest. A family paid 99,000...Ch. 3.1 - Present value. Solving A = Pert for P, we obtain...Ch. 3.1 - Present value. Referring to Problem 33, in how...Ch. 3.1 - Doubling time. How long will it take money to...Ch. 3.1 - Doubling time. How long will it take money to...Ch. 3.1 - Doubling rate. At what nominal rate compounded...Ch. 3.1 - Doubling rate. At what nominal rate compounded...Ch. 3.1 - Growth time. A man with 20,000 to invest decides...Ch. 3.1 - Growth time. A woman invests 5,000 in an account...Ch. 3.1 - Doubling times. (A) Show that the doubling time t...Ch. 3.1 - Doubling rates. (A) Show that the rate r that...Ch. 3.1 - Radioactive decay. A mathematical model for the...Ch. 3.1 - Radioactive decay. The continuous compound rate of...Ch. 3.1 - Radioactive decay. A cesium isotope has a...Ch. 3.1 - Prob. 46ECh. 3.1 - World population. A mathematical model for world...Ch. 3.1 - Prob. 48ECh. 3.1 - Population growth. Some underdeveloped nations...Ch. 3.1 - Population growth. Some developed nations have...Ch. 3.2 - Matched Problem 1 Find f(x) for (A) f(x) = 4ex +...Ch. 3.2 - Matched Problem 2 Find y for (A) y = 10x3 100 ln...Ch. 3.2 - Matched Problem 3 Find g(x) for (A) g(x) = x10 +...Ch. 3.2 - Matched Problem 4 The store in Example 4 also...Ch. 3.2 - Matched Problem 5 An investment of 5,000 earns...Ch. 3.2 - Prob. 6MPCh. 3.2 - Explore and Discuss 1 Complete Table 1. Do your...Ch. 3.2 - Explore and Discuss 2 (A) The graphs of f(x) =...Ch. 3.2 - In Problems 16, solve for the variable without...Ch. 3.2 - In Problems 16, solve for the variable without...Ch. 3.2 - In Problems 16, solve for the variable without...Ch. 3.2 - In Problems 16, solve for the variable without...Ch. 3.2 - In Problems 16, solve for the variable without...Ch. 3.2 - In Problems 16, solve for the variable without...Ch. 3.2 - In Problems 712, use logarithmic properties to...Ch. 3.2 - In Problems 712, use logarithmic properties to...Ch. 3.2 - In Problems 712, use logarithmic properties to...Ch. 3.2 - In Problems 712, use logarithmic properties to...Ch. 3.2 - In Problems 712, use logarithmic properties to...Ch. 3.2 - Prob. 12ECh. 3.2 - In Problems 1330, find f(x). 13. f(x) = 5ex + 3x +...Ch. 3.2 - In Problems 1330, find f(x). 14. f(x) = 7ex 2x +...Ch. 3.2 - In Problems 1330, find f(x). 15. f(x) = 2 ln x +...Ch. 3.2 - In Problems 1330, find f(x). 16. f(x) = 6 ln x x3...Ch. 3.2 - In Problems 1330, find f(x). 17. f(x) = x3 6exCh. 3.2 - In Problems 1330, find f(x). 18. f(x) = 9ex + 2x2Ch. 3.2 - In Problems 1330, find f(x). 19. f(x) = ex + x ln...Ch. 3.2 - In Problems 1330, find f(x). 20. f(x) = ln x + 2ex...Ch. 3.2 - In Problems 1330, find f(x). 21. f(x) = ln x3Ch. 3.2 - In Problems 1330, find f(x). 22. f(x) = ln x8Ch. 3.2 - In Problems 1330, find f(x). 23. f(x) = 5x ln x5Ch. 3.2 - In Problems 1330, find f(x). 24. f(x) = 4 + ln x9Ch. 3.2 - In Problems 1330, find f(x). 25. f(x) = ln x2 +...Ch. 3.2 - In Problems 1330, find f(x). 26. f(x) = ln x10 + 2...Ch. 3.2 - In Problems 1330, find f(x). 27. f(x) = ex + xeCh. 3.2 - In Problems 1330, find f(x). 28. f(x) = 3xe 2exCh. 3.2 - In Problems 1330, find f(x). 29. f(x) = xxeCh. 3.2 - In Problems 1330, find f(x). 30. f(x) = eexCh. 3.2 - In Problems 3138, find the equation of the line...Ch. 3.2 - In Problems 3138, find the equation of the line...Ch. 3.2 - In Problems 3138, find the equation of the line...Ch. 3.2 - In Problems 3138, find the equation of the line...Ch. 3.2 - In Problems 3138, find the equation of the line...Ch. 3.2 - f(x) = 1 + ln x4; x = eCh. 3.2 - In Problems 3138, find the equation of the line...Ch. 3.2 - In Problems 3138, find the equation of the line...Ch. 3.2 - A student claims that the line tangent to the...Ch. 3.2 - Refer to Problem 39. Does the line tangent to the...Ch. 3.2 - A student claims that the line tangent to the...Ch. 3.2 - Refer to Problem 41. Does the line tangent to the...Ch. 3.2 - In Problems 4346, first use appropriate properties...Ch. 3.2 - In Problems 4346, first use appropriate properties...Ch. 3.2 - In Problems 4346, first use appropriate properties...Ch. 3.2 - In Problems 4346, first use appropriate properties...Ch. 3.2 - In Problems 4758, find dydx for the indicated...Ch. 3.2 - In Problems 4758, find dydx for the indicated...Ch. 3.2 - In Problems 4758, find dydx for the indicated...Ch. 3.2 - In Problems 4758, find dydx for the indicated...Ch. 3.2 - In Problems 4758, find dydx for the indicated...Ch. 3.2 - In Problems 4758, find dydx for the indicated...Ch. 3.2 - In Problems 4758, find dydx for the indicated...Ch. 3.2 - In Problems 4758, find dydx for the indicated...Ch. 3.2 - In Problems 4758, find dydx for the indicated...Ch. 3.2 - In Problems 4758, find dydx for the indicated...Ch. 3.2 - In Problems 4758, find dydx for the indicated...Ch. 3.2 - In Problems 4758, find dydx for the indicated...Ch. 3.2 - Prob. 59ECh. 3.2 - Prob. 60ECh. 3.2 - In Problems 5964, use graphical approximation...Ch. 3.2 - Prob. 62ECh. 3.2 - In Problems 5964, use graphical approximation...Ch. 3.2 - In Problems 5964, use graphical approximation...Ch. 3.2 - Explain why limh0ech1h=c.Ch. 3.2 - Prob. 66ECh. 3.2 - Salvage value. The estimated salvage value S (in...Ch. 3.2 - Resale value. The estimated resale value R (in...Ch. 3.2 - Bacterial growth. A single cholera bacterium...Ch. 3.2 - Prob. 70ECh. 3.2 - Blood pressure. An experiment was set up to find a...Ch. 3.2 - Prob. 72ECh. 3.2 - Psychology: stimulus/response. In psychology, the...Ch. 3.2 - Psychology: learning. A mathematical model for the...Ch. 3.2 - Continuous compound interest. An investment of...Ch. 3.2 - Continuous compound interest. An investment of...Ch. 3.3 - Matched Problem 1 Use two different methods to...Ch. 3.3 - Matched Problem 2 Repeat Example 2 for f(x) = (2x...Ch. 3.3 - Matched Problem 3 Find f(x) for (A) f(x) = 5x8 ex...Ch. 3.3 - Matched Problem 4 Find (A) f(x) for f(x)=2xx2+3...Ch. 3.3 - Matched Problem 5 Find f(x) for (A) f(x)=x3ex+2...Ch. 3.3 - Matched Problem 6 Refer to Example 6. Suppose that...Ch. 3.3 - Explore and Discuss 1 Let F(x) = x2, S(x) = x3,...Ch. 3.3 - Explore and Discuss 2 Let T(x) = x5, B(x) = x2,...Ch. 3.3 - In Problems 14, find (A) the derivative of...Ch. 3.3 - Prob. 2ECh. 3.3 - Prob. 3ECh. 3.3 - In Problems 14, find (A) the derivative of...Ch. 3.3 - In Problems 58, find (A) the derivative of...Ch. 3.3 - In Problems 58, find (A) the derivative of...Ch. 3.3 - Prob. 7ECh. 3.3 - Prob. 8ECh. 3.3 - In Problems 934, find f(x) and simplify. 9. f(x) =...Ch. 3.3 - In Problems 934, find f(x) and simplify. 10. f(x)...Ch. 3.3 - In Problems 934, find f(x) and simplify. 11. f(x)...Ch. 3.3 - In Problems 934, find f(x) and simplify. 12. f(x)...Ch. 3.3 - In Problems 934, find f(x) and simplify. 13....Ch. 3.3 - In Problems 934, find f(x) and simplify. 14....Ch. 3.3 - In Problems 934, find f(x) and simplify. 15....Ch. 3.3 - In Problems 934, find f(x) and simplify. 16....Ch. 3.3 - In Problems 934, find f(x) and simplify. 17. f(x)...Ch. 3.3 - In Problems 934, find f(x) and simplify. 18. f(x)...Ch. 3.3 - In Problems 934, find f(x) and simplify. 19. f(x)...Ch. 3.3 - In Problems 934, find f(x) and simplify. 20. f(x)...Ch. 3.3 - In Problems 934, find f(x) and simplify. 21. f(x)...Ch. 3.3 - In Problems 934, find f(x) and simplify. 22. f(x)...Ch. 3.3 - In Problems 934, find f(x) and simplify. 23. f(x)...Ch. 3.3 - In Problems 934, find f(x) and simplify. 24. f(x)...Ch. 3.3 - In Problems 934, find f(x) and simplify. 25....Ch. 3.3 - In Problems 934, find f(x) and simplify. 26....Ch. 3.3 - In Problems 934, find f(x) and simplify. 27. f(x)...Ch. 3.3 - In Problems 934, find f(x) and simplify. 28. f(x)...Ch. 3.3 - In Problems 934, find f(x) and simplify. 29....Ch. 3.3 - In Problems 934, find f(x) and simplify. 30....Ch. 3.3 - In Problems 934, find f(x) and simplify. 31....Ch. 3.3 - In Problems 934, find f(x) and simplify. 32....Ch. 3.3 - In Problems 934, find f(x) and simplify. 33....Ch. 3.3 - In Problems 934, find f(x) and simplify. 34....Ch. 3.3 - In Problems 3546, find h(x), where f(x) is an...Ch. 3.3 - In Problems 3546, find h(x), where f(x) is an...Ch. 3.3 - In Problems 3546, find h(x), where f(x) is an...Ch. 3.3 - In Problems 3546, find h(x), where f(x) is an...Ch. 3.3 - In Problems 3546, find h(x), where f(x) is an...Ch. 3.3 - In Problems 3546, find h(x), where f(x) is an...Ch. 3.3 - In Problems 3546, find h(x), where f(x) is an...Ch. 3.3 - In Problems 3546, find h(x), where f(x) is an...Ch. 3.3 - In Problems 3546, find h(x), where f(x) is an...Ch. 3.3 - In Problems 3546, find h(x), where f(x) is an...Ch. 3.3 - In Problems 3546, find h(x), where f(x) is an...Ch. 3.3 - In Problems 3546, find h(x), where f(x) is an...Ch. 3.3 - In Problems 4756, find the indicated derivatives...Ch. 3.3 - In Problems 4756, find the indicated derivatives...Ch. 3.3 - In Problems 4756, find the indicated derivatives...Ch. 3.3 - In Problems 4756, find the indicated derivatives...Ch. 3.3 - In Problems 4756, find the indicated derivatives...Ch. 3.3 - In Problems 4756, find the indicated derivatives...Ch. 3.3 - In Problems 4756, find the indicated derivatives...Ch. 3.3 - In Problems 4756, find the indicated derivatives...Ch. 3.3 - In Problems 4756, find the indicated derivatives...Ch. 3.3 - In Problems 4756, find the indicated derivatives...Ch. 3.3 - In Problems 5760: (A) Find f(x) using the quotient...Ch. 3.3 - In Problems 5760: (A) Find f(x) using the quotient...Ch. 3.3 - In Problems 5760: (A) Find f(x) using the quotient...Ch. 3.3 - In Problems 5760: (A) Find f(x) using the quotient...Ch. 3.3 - In Problems 6166, find f(x) and find the equation...Ch. 3.3 - In Problems 6166, find f(x) and find the equation...Ch. 3.3 - In Problems 6166, find f(x) and find the equation...Ch. 3.3 - In Problems 6166, find f(x) and find the equation...Ch. 3.3 - In Problems 6166, find f(x) and find the equation...Ch. 3.3 - In Problems 6166, find f(x) and find the equation...Ch. 3.3 - In Problems 6770, find f(x) and find the value(s)...Ch. 3.3 - In Problems 6770, find f(x) and find the value(s)...Ch. 3.3 - In Problems 6770, find f(x) and find the value(s)...Ch. 3.3 - In Problems 6770, find f(x) and find the value(s)...Ch. 3.3 - In Problems 7174, find f(x) in two ways: (1) using...Ch. 3.3 - In Problems 7174, find f(x) in two ways: (1) using...Ch. 3.3 - In Problems 7174, find f(x) in two ways: (1) using...Ch. 3.3 - In Problems 7174, find f(x) in two ways: (1) using...Ch. 3.3 - In Problems 7592, find each indicated derivative...Ch. 3.3 - In Problems 7592, find each indicated derivative...Ch. 3.3 - In Problems 7592, find each indicated derivative...Ch. 3.3 - In Problems 7592, find each indicated derivative...Ch. 3.3 - In Problems 7592, find each indicated derivative...Ch. 3.3 - In Problems 7592, find each indicated derivative...Ch. 3.3 - In Problems 7592, find each indicated derivative...Ch. 3.3 - In Problems 7592, find each indicated derivative...Ch. 3.3 - In Problems 7592, find each indicated derivative...Ch. 3.3 - In Problems 7592, find each indicated derivative...Ch. 3.3 - In Problems 7592, find each indicated derivative...Ch. 3.3 - In Problems 7592, find each indicated derivative...Ch. 3.3 - Prob. 87ECh. 3.3 - Prob. 88ECh. 3.3 - Prob. 89ECh. 3.3 - Prob. 90ECh. 3.3 - In Problems 7592, find each indicated derivative...Ch. 3.3 - In Problems 7592, find each indicated derivative...Ch. 3.3 - Sales analysis. The total sales S (in thousands)...Ch. 3.3 - Sales analysis. A communications company has...Ch. 3.3 - Pricedemand equation. According to economic...Ch. 3.3 - Pricesupply equation. According to economic...Ch. 3.3 - Prob. 97ECh. 3.3 - Prob. 98ECh. 3.4 - Matched Problem 1 Let f (u) = 2u and g(x) = ex....Ch. 3.4 - Matched Problem 2 Write each function as a...Ch. 3.4 - Matched Problem 3 Find the indicated derivatives:...Ch. 3.4 - Matched Problem 4 Find the derivative m(x) of the...Ch. 3.4 - Matched Problem 5 For y = h(x) = [ln(1 + ex) ]3,...Ch. 3.4 - Matched Problem 6 Find (A) ddxln(x3+2x) (B)...Ch. 3.4 - Explore and Discuss 1 Let u(x) = 2x2 and m(x) =...Ch. 3.4 - Explore and Discuss 2 Let m(x) = f[g(x)]. Use the...Ch. 3.4 - In Problems 18, find f(x). (If necessary, review...Ch. 3.4 - In Problems 18, find f(x). (If necessary, review...Ch. 3.4 - In Problems 18, find f(x). (If necessary, review...Ch. 3.4 - In Problems 18, find f(x). (If necessary, review...Ch. 3.4 - In Problems 18, find f(x). (If necessary, review...Ch. 3.4 - In Problems 18, find f(x). (If necessary, review...Ch. 3.4 - In Problems 18, find f(x). (If necessary, review...Ch. 3.4 - Prob. 8ECh. 3.4 - In Problems 916, replace ? with an expression that...Ch. 3.4 - In Problems 916, replace ? with an expression that...Ch. 3.4 - In Problems 916, replace ? with an expression that...Ch. 3.4 - In Problems 916, replace ? with an expression that...Ch. 3.4 - In Problems 916, replace ? with an expression that...Ch. 3.4 - In Problems 916, replace ? with an expression that...Ch. 3.4 - In Problems 916, replace ? with an expression that...Ch. 3.4 - In Problems 916, replace ? with an expression that...Ch. 3.4 - In Problems 1734, find f(x) and simplify. 17. f(x)...Ch. 3.4 - In Problems 1734, find f(x) and simplify. 18. f(x)...Ch. 3.4 - In Problems 1734, find f(x) and simplify. 19. f(x)...Ch. 3.4 - In Problems 1734, find f(x) and simplify. 20. f(x)...Ch. 3.4 - In Problems 1734, find f(x) and simplify. 21. f(x)...Ch. 3.4 - In Problems 1734, find f(x) and simplify. 22. f(x)...Ch. 3.4 - In Problems 1734, find f(x) and simplify. 23. f(x)...Ch. 3.4 - In Problems 1734, find f(x) and simplify. 24. f(x)...Ch. 3.4 - In Problems 1734, find f(x) and simplify. 25. f(x)...Ch. 3.4 - In Problems 1734, find f(x) and simplify. 26....Ch. 3.4 - In Problems 1734, find f(x) and simplify. 27. f(x)...Ch. 3.4 - In Problems 1734, find f(x) and simplify. 28. f(x)...Ch. 3.4 - In Problems 1734, find f(x) and simplify. 29. f(x)...Ch. 3.4 - In Problems 1734, find f(x) and simplify. 30. f(x)...Ch. 3.4 - In Problems 1734, find f(x) and simplify. 31. f(x)...Ch. 3.4 - In Problems 1734, find f(x) and simplify. 32. f(x)...Ch. 3.4 - In Problems 1734, find F(x) and simplify. 33. f(x)...Ch. 3.4 - In Problems 1734, find f(x) and simplify. 34. f(x)...Ch. 3.4 - In Problems 3540, find f(x) and the equation of...Ch. 3.4 - In Problems 3540, find f(x) and the equation of...Ch. 3.4 - In Problems 3540, find f(x) and the equation of...Ch. 3.4 - In Problems 3540, find f(x) and the equation of...Ch. 3.4 - In Problems 3540, find f(x) and the equation of...Ch. 3.4 - In Problems 3540, find f(x) and the equation of...Ch. 3.4 - In Problems 4156, find the indicated derivative...Ch. 3.4 - In Problems 4156, find the indicated derivative...Ch. 3.4 - In Problems 4156, find the indicated derivative...Ch. 3.4 - In Problems 4156, find the indicated derivative...Ch. 3.4 - In Problems 4156, find the indicated derivative...Ch. 3.4 - In Problems 4156, find the indicated derivative...Ch. 3.4 - In Problems 4156, find the indicated derivative...Ch. 3.4 - In Problems 4156, find the indicated derivative...Ch. 3.4 - In Problems 4156, find the indicated derivative...Ch. 3.4 - Prob. 50ECh. 3.4 - In Problems 4156, find the indicated derivative...Ch. 3.4 - In Problems 4156, find the indicated derivative...Ch. 3.4 - In Problems 4156, find the indicated derivative...Ch. 3.4 - In Problems 4156, find the indicated derivative...Ch. 3.4 - In Problems 4156, find the indicated derivative...Ch. 3.4 - In Problems 4156, find the indicated derivative...Ch. 3.4 - In Problems 5762, find f(x) and find the equation...Ch. 3.4 - In Problems 5762, find f(x) and find the equation...Ch. 3.4 - In Problems 5762, find f(x) and find the equation...Ch. 3.4 - In Problems 5762, find f(x) and find the equation...Ch. 3.4 - In Problems 5762, find f(x) and find the equation...Ch. 3.4 - In Problems 5762, find f (x) and find the equation...Ch. 3.4 - In Problems 6368, find f(x) and find, the value(s)...Ch. 3.4 - In Problems 6368, find f(x) and find, the value(s)...Ch. 3.4 - In Problems 6368, find f(x) and find, the value(s)...Ch. 3.4 - In Problems 6368, find f(x) and find, the value(s)...Ch. 3.4 - In Problems 6368, find f(x) and find, the value(s)...Ch. 3.4 - In Problems 6368, find f(x) and find, the value(s)...Ch. 3.4 - A student reasons that the functions f(x) = ln[5...Ch. 3.4 - A student reasons that the function f(x) = (x +...Ch. 3.4 - Prob. 71ECh. 3.4 - Prob. 72ECh. 3.4 - Prob. 73ECh. 3.4 - Prob. 74ECh. 3.4 - In Problems 7178, give the domain of f, the domain...Ch. 3.4 - Prob. 76ECh. 3.4 - In Problems 7178, give the domain of f, the domain...Ch. 3.4 - In Problems 7178, give the domain of f, the domain...Ch. 3.4 - In Problems 7990, find each derivative and...Ch. 3.4 - In Problems 7990, find each derivative and...Ch. 3.4 - In Problems 7990, find each derivative and...Ch. 3.4 - In Problems 7990, find each derivative and...Ch. 3.4 - In Problems 7990, find each derivative and...Ch. 3.4 - In Problems 7990, find each derivative and...Ch. 3.4 - In Problems 7990, find each derivative and...Ch. 3.4 - Prob. 86ECh. 3.4 - In Problems 7990, find each derivative and...Ch. 3.4 - In Problems 7990, find each derivative and...Ch. 3.4 - In Problems 7990, find each derivative and...Ch. 3.4 - Prob. 90ECh. 3.4 - Cost function. The total cost (in hundreds of...Ch. 3.4 - Cost function. The total cost (in hundreds of...Ch. 3.4 - Pricesupply equation. The number x of bicycle...Ch. 3.4 - Pricedemand equation. The number x of bicycle...Ch. 3.4 - Drug concentration. The drug concentration in the...Ch. 3.4 - Prob. 96ECh. 3.4 - Blood pressure and age. A research group using...Ch. 3.4 - Prob. 98ECh. 3.5 - Matched Problem 1 Graph x2 + y2 169 = 0, find y...Ch. 3.5 - Matched Problem 2 Repeat Example 2 for x2 + y2 xy...Ch. 3.5 - Matched Problem 3 Find x for x = x(t) defined...Ch. 3.5 - Prob. 1EDCh. 3.5 - In Problems 18, if it is possible to solve for y...Ch. 3.5 - In Problems 18, if it is possible to solve for y...Ch. 3.5 - In Problems 18, if it is possible to solve for y...Ch. 3.5 - In Problems 18, if it is possible to solve for y...Ch. 3.5 - In Problems 18, if it is possible to solve for y...Ch. 3.5 - In Problems 18, if it is possible to solve for y...Ch. 3.5 - In Problems 18, if it is possible to solve for y...Ch. 3.5 - Prob. 8ECh. 3.5 - In Problems 916, find y in two ways: (A)...Ch. 3.5 - In Problems 916, find y in two ways: (A)...Ch. 3.5 - In Problems 916, find y in two ways: (A)...Ch. 3.5 - In Problems 916, find y in two ways: (A)...Ch. 3.5 - In Problems 916, find y in two ways: (A)...Ch. 3.5 - Prob. 14ECh. 3.5 - In Problems 916, find y in two ways: (A)...Ch. 3.5 - In Problems 916, find y in two ways: (A)...Ch. 3.5 - In Problems 1734, use implicit, differentiation to...Ch. 3.5 - In Problems 1734, use implicit, differentiation to...Ch. 3.5 - In Problems 1734, use implicit, differentiation to...Ch. 3.5 - In Problems 1734, use implicit, differentiation to...Ch. 3.5 - In Problems 1734, use implicit, differentiation to...Ch. 3.5 - In Problems 1734, use implicit, differentiation to...Ch. 3.5 - In Problems 1734, use implicit, differentiation to...Ch. 3.5 - In Problems 1734, use implicit, differentiation to...Ch. 3.5 - In Problems 1734, use implicit, differentiation to...Ch. 3.5 - In Problems 1734, use implicit, differentiation to...Ch. 3.5 - In Problems 1734, use implicit, differentiation to...Ch. 3.5 - In Problems 1734, use implicit, differentiation to...Ch. 3.5 - In Problems 1734, use implicit, differentiation to...Ch. 3.5 - In Problems 1734, use implicit, differentiation to...Ch. 3.5 - In Problems 1734, use implicit, differentiation to...Ch. 3.5 - In Problems 1734, use implicit, differentiation to...Ch. 3.5 - In Problems 1734, use implicit, differentiation to...Ch. 3.5 - In Problems 1734, use implicit, differentiation to...Ch. 3.5 - In Problems 35 and 36, find x for x = x(t) defined...Ch. 3.5 - In Problems 35 and 36, find x for x = x(t) defined...Ch. 3.5 - Problems 37 and 38 refer to the equation and graph...Ch. 3.5 - Problems 37 and 38 refer to the equation and graph...Ch. 3.5 - In Problems 3942, find the equation(s) of the...Ch. 3.5 - In Problems 3942, find the equation(s) of the...Ch. 3.5 - In Problems 3942, find the equation(s) of the...Ch. 3.5 - In Problems 3942, find the equation(s) of the...Ch. 3.5 - If xey = 1, find y in two ways, first by...Ch. 3.5 - Prob. 44ECh. 3.5 - In Problems 4552, find y and the slope of the...Ch. 3.5 - In Problems 4552, find y and the slope of the...Ch. 3.5 - In Problems 4552, find y and the slope of the...Ch. 3.5 - Prob. 48ECh. 3.5 - In Problems 4552, find y and the slope of the...Ch. 3.5 - In Problems 4552, find y and the slope of the...Ch. 3.5 - In Problems 4552, find y and the slope of the...Ch. 3.5 - In Problems 4552, find y and the slope of the...Ch. 3.5 - Find the equation(s) of the tangent line(s) at the...Ch. 3.5 - Refer to the equation in Problem 53. Find the...Ch. 3.5 - Pricesupply equation. The number x of fitness...Ch. 3.5 - Pricedemand equation. The number x of fitness...Ch. 3.5 - Pricedemand equation. The number x of compact...Ch. 3.5 - Pricesupply equation. The number x of compact...Ch. 3.5 - Biophysics. In biophysics, the equation...Ch. 3.5 - Biophysics. In Problem 59, find dV/dL by implicit...Ch. 3.5 - Speed of sound. The speed of sound in air is given...Ch. 3.5 - Gravity. The equation F=Gm1m2r2 is Newtons law of...Ch. 3.5 - Speed of sound. Refer to Problem 61. Find dvdT and...Ch. 3.5 - Gravity. Refer to Problem 62. Find dFdr and...Ch. 3.6 - Matched Problem 1 Again, a 26-foot ladder is...Ch. 3.6 - Matched Problem 2 Repeat Example 2 for the same...Ch. 3.6 - Prob. 3MPCh. 3.6 - Matched Problem 4 Repeat Example 4 for a...Ch. 3.6 - Prob. 1EDCh. 3.6 - For Problems 18, review the geometric formulas in...Ch. 3.6 - Prob. 2ECh. 3.6 - For Problems 18, review the geometric formulas in...Ch. 3.6 - For Problems 18, review the geometric formulas in...Ch. 3.6 - For Problems 18, review the geometric formulas in...Ch. 3.6 - For Problems 18, review the geometric formulas in...Ch. 3.6 - Prob. 7ECh. 3.6 - Prob. 8ECh. 3.6 - In Problems 914, assume that x = x(t) and y =...Ch. 3.6 - In Problems 914, assume that x = x(t) and y =...Ch. 3.6 - In Problems 914, assume that x = x(t) and y =...Ch. 3.6 - In Problems 914, assume that x = x(t) and y =...Ch. 3.6 - In Problems 914, assume that x = x(t) and y =...Ch. 3.6 - In Problems 914, assume that x = x(t) and y =...Ch. 3.6 - A point is moving on the graph of xy = 36. When...Ch. 3.6 - A point is moving on the graph of 4x2 + 9y2 = 36....Ch. 3.6 - A boat is being pulled toward a dock as shown in...Ch. 3.6 - Refer to Problem 17. Suppose that the distance...Ch. 3.6 - Prob. 19ECh. 3.6 - Refer to Problem 19. How fast is the circumference...Ch. 3.6 - Prob. 21ECh. 3.6 - Refer to Problem 21. How fast is the surface area...Ch. 3.6 - Boyles law for enclosed gases states that if the...Ch. 3.6 - Boyles law for enclosed gases states that if the...Ch. 3.6 - A 10-foot ladder is placed against a vertical...Ch. 3.6 - A weather balloon is rising vertically at the rate...Ch. 3.6 - A streetlight is on top of a 20-foot pole. A...Ch. 3.6 - Refer to Problem 27. At what rate is the persons...Ch. 3.6 - Helium is pumped into a spherical balloon at a...Ch. 3.6 - A point is moving along the x axis at a constant...Ch. 3.6 - Prob. 31ECh. 3.6 - A point is moving on the graph of x3 + y2 = 1 in...Ch. 3.6 - Cost, revenue, and profit rates. Suppose that for...Ch. 3.6 - Cost, revenue, and profit rates. Repeat Problem 33...Ch. 3.6 - Advertising. A retail store estimates that weekly...Ch. 3.6 - Advertising. Repeat Problem 35 for...Ch. 3.6 - Prob. 37ECh. 3.6 - Pricedemand. The price p (in dollars) and demand x...Ch. 3.6 - Revenue. Refer to Problem 37. Find the associated...Ch. 3.6 - Revenue. Refer to Problem 38. Find the associated...Ch. 3.6 - Pricesupply equation. The price p (in dollars per...Ch. 3.6 - Pricesupply equation. The price p (in dollars) and...Ch. 3.6 - Prob. 43ECh. 3.6 - Prob. 44ECh. 3.6 - Pricedemand. The price p (in dollars) and demand x...Ch. 3.6 - Pricedemand. Repeat Problem 45 for...Ch. 3.6 - Prob. 47ECh. 3.6 - Learning. A person who is new on an assembly line...Ch. 3.7 - Matched Problem 1 A model for the population data...Ch. 3.7 - Matched Problem 2 Find E(p) for the pricedemand...Ch. 3.7 - Matched Problem 3 Repeat Example 3 if the current...Ch. 3.7 - Explore and Discuss 1 A broker is trying to sell...Ch. 3.7 - Prob. 2EDCh. 3.7 - In Problems 18, use the given equation, which...Ch. 3.7 - In Problems 18, use the given equation, which...Ch. 3.7 - In Problems 18, use the given equation, which...Ch. 3.7 - In Problems 18, use the given equation, which...Ch. 3.7 - In Problems 18, use the given equation, which...Ch. 3.7 - In Problems 18, use the given equation, which...Ch. 3.7 - In Problems 18, use the given equation, which...Ch. 3.7 - In Problems 18, use the given equation, which...Ch. 3.7 - In Problems 914, find the relative rate of change...Ch. 3.7 - In Problems 914, find the relative rate of change...Ch. 3.7 - In Problems 914, find the relative rate of change...Ch. 3.7 - In Problems 914, find the relative rate of change...Ch. 3.7 - In Problems 914, find the relative rate of change...Ch. 3.7 - In Problems 914, find the relative rate of change...Ch. 3.7 - In Problems 1524. find the relative rate of change...Ch. 3.7 - In Problems 1524. find the relative rate of change...Ch. 3.7 - In Problems 1524. find the relative rate of change...Ch. 3.7 - In Problems 1524. find the relative rate of change...Ch. 3.7 - In Problems 1524. find the relative rate of change...Ch. 3.7 - In Problems 1524. find the relative rate of change...Ch. 3.7 - In Problems 1524. find the relative rate of change...Ch. 3.7 - In Problems 1524. find the relative rate of change...Ch. 3.7 - In Problems 1524. find the relative rate of change...Ch. 3.7 - In Problems 1524. find the relative rate of change...Ch. 3.7 - In Problems 2532, find the percentage rate of...Ch. 3.7 - In Problems 2532, find the percentage rate of...Ch. 3.7 - In Problems 2532, find the percentage rate of...Ch. 3.7 - In Problems 2532, find the percentage rate of...Ch. 3.7 - In Problems 2532, find the percentage rate of...Ch. 3.7 - In Problems 2532, find the percentage rate of...Ch. 3.7 - In Problems 2532, find the percentage rate of...Ch. 3.7 - Prob. 32ECh. 3.7 - In Problems 3338, use the pricedemand equation to...Ch. 3.7 - In Problems 3338, use the pricedemand equation to...Ch. 3.7 - In Problems 3338, use the pricedemand equation to...Ch. 3.7 - In Problems 3338, use the pricedemand equation to...Ch. 3.7 - In Problems 3338, use the pricedemand equation to...Ch. 3.7 - In Problems 3338, use the pricedemand equation to...Ch. 3.7 - In Problems 3946, find the logarithmic derivative....Ch. 3.7 - In Problems 3946, find the logarithmic derivative....Ch. 3.7 - In Problems 3946, find the logarithmic derivative....Ch. 3.7 - Prob. 42ECh. 3.7 - In Problems 3946, find the logarithmic derivative....Ch. 3.7 - In Problems 3946, find the logarithmic derivative....Ch. 3.7 - In Problems 3946, find the logarithmic derivative....Ch. 3.7 - In Problems 3946, find the logarithmic derivative....Ch. 3.7 - In Problems 4750, use the pricedemand equation to...Ch. 3.7 - In Problems 4750, use the pricedemand equation to...Ch. 3.7 - In Problems 4750, use the pricedemand equation to...Ch. 3.7 - In Problems 4750, use the pricedemand equation to...Ch. 3.7 - In Problems 5158, use the pricedemand equation p +...Ch. 3.7 - In Problems 5158, use the pricedemand equation p +...Ch. 3.7 - In Problems 5158, use the pricedemand equation p +...Ch. 3.7 - Prob. 54ECh. 3.7 - In Problems 5158, use the pricedemand equation p +...Ch. 3.7 - In Problems 5158, use the pricedemand equation p +...Ch. 3.7 - In Problems 5158, use the pricedemand equation p +...Ch. 3.7 - In Problems 5158, use the pricedemand equation p +...Ch. 3.7 - In Problems 5966, use the pricedemand equation to...Ch. 3.7 - In Problems 5966, use the pricedemand equation to...Ch. 3.7 - In Problems 5966, use the pricedemand equation to...Ch. 3.7 - In Problems 5966, use the pricedemand equation to...Ch. 3.7 - In Problems 5966, use the pricedemand equation to...Ch. 3.7 - Prob. 64ECh. 3.7 - Prob. 65ECh. 3.7 - In Problems 5966, use the pricedemand equation to...Ch. 3.7 - In Problems 6772, use the demand equation to find...Ch. 3.7 - In Problems 6772, use the demand equation to find...Ch. 3.7 - In Problems 6772, use the demand equation to find...Ch. 3.7 - In Problems 6772, use the demand equation to find...Ch. 3.7 - In Problems 6772, use the demand equation to find...Ch. 3.7 - Prob. 72ECh. 3.7 - Prob. 73ECh. 3.7 - Prob. 74ECh. 3.7 - In Problems 7376, use the pricedemand equation to...Ch. 3.7 - In Problems 7376, use the pricedemand equation to...Ch. 3.7 - Prob. 77ECh. 3.7 - Prob. 78ECh. 3.7 - In Problems 7780. use the pricedemand equation to...Ch. 3.7 - In Problems 7780. use the pricedemand equation to...Ch. 3.7 - Prob. 81ECh. 3.7 - Find E(p) for x = f(p) = Aekp, where A and k are...Ch. 3.7 - Rate of change of cost. A fast-food restaurant can...Ch. 3.7 - Rate of change of cost. The fast-food restaurant...Ch. 3.7 - Revenue and elasticity. The pricedemand equation...Ch. 3.7 - Revenue and elasticity. Refer to Problem 85. If...Ch. 3.7 - Revenue and elasticity. The pricedemand equation...Ch. 3.7 - Revenue and elasticity. Refer to Problem 87. If...Ch. 3.7 - Maximum revenue. Refer to Problem 85. What price...Ch. 3.7 - Maximum revenue. Refer to Problem 87. What price...Ch. 3.7 - Population growth. A model for Canadas population...Ch. 3.7 - Prob. 92ECh. 3.7 - Crime. A model for the number of robberies per...Ch. 3.7 - Prob. 94ECh. 3 - Use a calculator to evaluate A = 2,000e0.09t to...Ch. 3 - In Problems 25, find the indicated derivative. 2....Ch. 3 - In Problems 25, find the indicated derivative. 3....Ch. 3 - Prob. 4RECh. 3 - In Problems 25, find the indicated derivative. 5....Ch. 3 - Find y for y = y(x) defined implicity by the...Ch. 3 - Prob. 7RECh. 3 - Prob. 8RECh. 3 - Prob. 9RECh. 3 - In Problems 812, use the pricedemand equation 2p +...Ch. 3 - Prob. 11RECh. 3 - Prob. 12RECh. 3 - Find the slope of the line tangent to y = 100e0.1x...Ch. 3 - Use a calculator and a table of values to...Ch. 3 - Find the indicated derivatives in Problems 1520....Ch. 3 - Prob. 16RECh. 3 - Find the indicated derivatives in Problems 1520....Ch. 3 - Find the indicated derivatives in Problems 1520....Ch. 3 - Find the indicated derivatives in Problems 1520....Ch. 3 - Find the indicated derivatives in Problems 1520....Ch. 3 - Find the equation of the line tangent to the graph...Ch. 3 - Find y for y = y(x) defined implicitly by the...Ch. 3 - Find x for x = x(t) defined implicitly by x3 2t2x...Ch. 3 - Find y for y = y(x) defined implicitly by x y2 =...Ch. 3 - Find y for y = y(x) defined implicitly by ln y =...Ch. 3 - In Problems 2628, find the logarithmic...Ch. 3 - In Problems 2628, find the logarithmic...Ch. 3 - In Problems 2628, find the logarithmic...Ch. 3 - A point is moving on the graph of y2 4x2 = 12 so...Ch. 3 - A 17-foot ladder is placed against a wall. If the...Ch. 3 - Prob. 31RECh. 3 - Find the values of p for which demand is elastic...Ch. 3 - Graph the revenue function as a function of price...Ch. 3 - Prob. 34RECh. 3 - Find the indicated derivatives in Problems 3537....Ch. 3 - Prob. 36RECh. 3 - Find the indicated derivatives in Problems 3537....Ch. 3 - Find y for y = y(x) defined implicitly by the...Ch. 3 - A rock thrown into a still pond causes a circular...Ch. 3 - Prob. 40RECh. 3 - Doubling time. How long will it take money to...Ch. 3 - Continuous compound interest. If 100 is invested...Ch. 3 - Continuous compound interest. If 12,000 is...Ch. 3 - Prob. 44RECh. 3 - Price-demand. Given the demand equation x=5,0002p3...Ch. 3 - Rate of change of revenue. A company is...Ch. 3 - Revenue and elasticity. The pricedemand equation...Ch. 3 - Average income. A model for the average income per...Ch. 3 - Drug concentration. The drug concentration in the...Ch. 3 - Wound healing. A circular wound on an arm is...Ch. 3 - Psychology: learning. In a computer assembly...Ch. 3 - Learning. A new worker on the production line...
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- 7.2.10arrow_forwardIn Problems 14–19, solve each equation. 14. 5*+2 = 125 15. log(x + 9) = 2 16. 8 - 2e* = 4 17. log(x + 3) = log (x + 6) 18. 7*+3 = e 19. log2(x – 4) + log2(x + 4) = 3arrow_forward8. Without a calculator, match the functions y = 2, y = eX, y = 3", y = In x, y = log x with the graphs in Figure 5.14. %3D y A B C D E Figure 5.14arrow_forward
- 30. The population of a species is given by the function 100000 P(t) 100900e-t where t is measured in years. What is the initial population and how long it will take the population to triple its initial size?arrow_forward9. The equation ( log3 x-e has = 3V3 %3D exactly three real solutions at least one real solutionsarrow_forward3. In an experiment, the growth rate of a population of bacteria t hours after the bacteria are exposed to moist air is approximated by k√t, where P dP dt represents the population size and k is a constant. The population of bacteria is 1,000 before the bacteria are exposed to moist air and the population grows to 1,200 after 4 hours. Find the population bacteria after 9 hours. -arrow_forward
- Solve the equations given in Problems 17 to 22. 17. logr - logr = log Sx– log2x 18. log2 - logt = log 16+fogt 19. 2logb2 – 3logb=log&b– log 4b 20. log(x+1)+log(x – 1) = log3 %3D 1 21. log 27=log(0.Sa) 22. log(x2 – 5) - logx = log4 %3Darrow_forward12. The following graph is the 2.5 acceleration versus time for the 2. motion of a bike. If the bike starts from the origin with initial velocity 4.0 m/s, what is the total 1.5 1 distance it travels during the 5.0 0.5 seconds of motion? 0 -0.5 -1 -1.5 t (s) (su) earrow_forward6. Solve the equation. Write the solution set with exact values give approximation to 4 decimal places. i. 25+1=4-3 il 7e4x - 2 = 12 iii. 5 In(x+2)+1=16 iv. -3+log+x= -log(x+30) v. In x + In(x-4)=In(3x - 10)arrow_forward
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