Calculus and Its Applications Plus MyLab Math with Pearson eText -- Access Card Package (11th Edition) (Bittinger, Ellenbogen & Surgent, The Calculus and Its Applications Series)
11th Edition
ISBN: 9780133795561
Author: Marvin L. Bittinger, David J. Ellenbogen, Scott J. Surgent
Publisher: PEARSON
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Textbook Question
Chapter 1.7, Problem 96E
The following is the beginning of an alternative proof of the
Proof: Let
Then
Therefore, …
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Use the information in the following table to find h' (a) at the given value for a.
x|f(x) g(x) f'(x) g(x)
0
0
0
4
3
1
4
4
3
0
2
7
1
2
7
3
3
1
2
9
4
0
4
5
7
h(x) = f(g(x)); a = 0
h' (0) =
Use the information in the following table to find h' (a) at the given value for a.
x f(x) g(x) f'(x) g'(x)
0
0
3
2
1
1
0
0
2
0
2
43
22
4
3
3
2
3
1
1
4
1
2
0
4
2
h(x) = (1/(2) ²;
9(x)
h' (3)=
=
; a=3
The position of a moving hockey puck after t seconds is s(t) = tan
a. Find the velocity of the hockey puck at any time t.
v(t)
=====
b. Find the acceleration of the puck at any time t.
-1
a (t)
=
(t) where s is in meters.
c. Evaluate v(t) and a (t) for t = 1, 4, and 5 seconds. Round to 4 decimal places, if necessary.
v (1)
v (4)
v (5)
a (1)
=
=
=
=
a (4) =
a (5) =
d. What conclusion can be drawn from the results in the previous part?
○ The hockey puck is decelerating/slowing down at 1, 4, and 5 seconds
○ The hockey puck has a constant velocity/speed at 1, 4, and 5 seconds
○ The hockey puck is accelerating/speeding up at 1, 4, and 5 seconds
Chapter 1 Solutions
Calculus and Its Applications Plus MyLab Math with Pearson eText -- Access Card Package (11th Edition) (Bittinger, Ellenbogen & Surgent, The Calculus and Its Applications Series)
Ch. 1.1 - Complete each of the following statements.
1. As x...Ch. 1.1 - Complete each of the following statements. As x...Ch. 1.1 - Complete each of the following statements. The...Ch. 1.1 - Complete each of the following statements.
4. The...Ch. 1.1 - Complete each of the following statements. The...Ch. 1.1 - Complete each of the following statements.
6. The...Ch. 1.1 - Complete each of the following statements.
7. The...Ch. 1.1 - Complete each of the following statements. The...Ch. 1.1 - Complete each of the following statements. The...Ch. 1.1 - Complete each of the following statements. The...
Ch. 1.1 - For Exercises 11 and 12, consider the function f...Ch. 1.1 - For Exercises 11 and 12, consider the function f...Ch. 1.1 - For Exercises 13 and 14, consider the function g...Ch. 1.1 - For Exercises 13 and 14, consider the function g...Ch. 1.1 - For Exercises 15–22, use the following graph of F...Ch. 1.1 - For Exercises 15–22, use the following graph of F...Ch. 1.1 - For Exercises 15–22, use the following graph of F...Ch. 1.1 - For Exercises 15–22, use the following graph of F...Ch. 1.1 - For Exercises 1522, use the following graph of F...Ch. 1.1 - For Exercises 15–22, use the following graph of F...Ch. 1.1 - For Exercises 15–22, use the following graph of F...Ch. 1.1 - For Exercises 1522, use the following graph of F...Ch. 1.1 - For Exercises 23-30, use the following graph of G...Ch. 1.1 - For Exercises 23-30, use the following graph of G...Ch. 1.1 - For Exercises 23-30, use the following graph of G...Ch. 1.1 - For Exercises 23-30, use the following graph of G...Ch. 1.1 - For Exercises 23-30, use the following graph of G...Ch. 1.1 - For Exercises 23-30, use the following graph of G...Ch. 1.1 - For Exercises 23-30, use the following graph of G...Ch. 1.1 - For Exercises 23-30, use the following graph of G...Ch. 1.1 - For Exercises 31–40, use the following graph of H...Ch. 1.1 - For Exercises 3140, use the following graph of H...Ch. 1.1 - For Exercises 3140, use the following graph of H...Ch. 1.1 - For Exercises 3140, use the following graph of H...Ch. 1.1 - For Exercises 3140, use the following graph of H...Ch. 1.1 - For Exercises 31–40, use the following graph of H...Ch. 1.1 - For Exercises 3140, use the following graph of H...Ch. 1.1 - For Exercises 31–40, use the following graph of H...Ch. 1.1 - For Exercises 31–40, use the following graph of H...Ch. 1.1 - For Exercises 3140, use the following graph of H...Ch. 1.1 - For Exercises 41-50, use the following graph of f...Ch. 1.1 - For Exercises 41-50, use the following graph of f...Ch. 1.1 - For Exercises 41-50, use the following graph of f...Ch. 1.1 - For Exercises 41-50, use the following graph of f...Ch. 1.1 - For Exercises 41-50, use the following graph of f...Ch. 1.1 - For Exercises 41-50, use the following graph of f...Ch. 1.1 - For Exercises 41-50, use the following graph of f...Ch. 1.1 - For Exercises 41-50, use the following graph of f...Ch. 1.1 - For Exercises 41-50, use the following graph of f...Ch. 1.1 - For Exercises 41-50, use the following graph of f...Ch. 1.1 - For Exercises 51-68, graph each function and then...Ch. 1.1 - For Exercises 51-68, graph each function and then...Ch. 1.1 - For Exercises 51-68, graph each function and then...Ch. 1.1 - For Exercises 51-68, graph each function and then...Ch. 1.1 - For Exercises 51-68, graph each function and then...Ch. 1.1 - For Exercises 51-68, graph each function and then...Ch. 1.1 - For Exercises 51-68, graph each function and then...Ch. 1.1 - For Exercises 51-68, graph each function and then...Ch. 1.1 - For Exercises 51-68, graph each function and then...Ch. 1.1 - For Exercises 51-68, graph each function and then...Ch. 1.1 - For Exercises 51-68, graph each function and then...Ch. 1.1 - For Exercises 51-68, graph each function and then...Ch. 1.1 - For Exercises 51-68, graph each function and then...Ch. 1.1 - For Exercises 51-68, graph each function and then...Ch. 1.1 - For Exercises 51-68, graph each function and then...Ch. 1.1 - For Exercises 51-68, graph each function and then...Ch. 1.1 - For Exercises 51-68, graph each function and then...Ch. 1.1 - For Exercises 51-68, graph each function and then...Ch. 1.1 - Business and Economics
Taxicab fares. In New York...Ch. 1.1 - Taxicab fares. In New York City, taxicabs change...Ch. 1.1 - Taxicab fares. In New York City, taxicabs change...Ch. 1.1 - The Postage function. The cost of sending a large...Ch. 1.1 - The Postage function.
The cost of sending a large...Ch. 1.1 - The Postage function. The cost of sending a large...Ch. 1.1 - The Postage function.
The cost of sending a large...Ch. 1.1 - The Postage function.
The cost of sending a large...Ch. 1.1 - Tax Rate Schedule. The federal tax rate for single...Ch. 1.1 - Tax Rate Schedule. The federal tax rate for single...Ch. 1.1 - Tax Rate Schedule. The federal tax rate for single...Ch. 1.1 - Tax Rate Schedule.
The federal tax rate for heads...Ch. 1.1 - Tax Rate Schedule.
The federal tax rate for heads...Ch. 1.1 - Tax Rate Schedule.
The federal tax rate for heads...Ch. 1.1 - In Exercises 83-58, fill in each blank so that...Ch. 1.1 - In Exercises 83-58, fill in each blank so that...Ch. 1.1 - In Exercises 83-58, fill in each blank so that...Ch. 1.1 - Graph the function f given by...Ch. 1.1 - In Exercises 87-89, use GRAFH and TRACE to find...Ch. 1.1 - In Exercises 87-89, use GRAFH and TRACE to find...Ch. 1.1 - In Exercises 87-89, use GRAFH and TRACE to find...Ch. 1.2 - Classify each statement as either true or...Ch. 1.2 - Prob. 2ECh. 1.2 - Classify each statement as either true or false....Ch. 1.2 - Classify each statement as either true or...Ch. 1.2 - Classify each statement as either true or false....Ch. 1.2 - Classify each statement as either true or false....Ch. 1.2 - Classify each statement as either true or...Ch. 1.2 - Classify each statement as either true or false....Ch. 1.2 - Use the theorem on limits of rational functions to...Ch. 1.2 - Use the theorem on limits of rational functions to...Ch. 1.2 - Use the theorem on limits of rational functions to...Ch. 1.2 - Use the theorem on limits of rational functions to...Ch. 1.2 - Use the theorem on limits of rational functions to...Ch. 1.2 - Use the theorem on limits of rational functions to...Ch. 1.2 - Use the theorem on limits of rational functions to...Ch. 1.2 - Use the theorem on limits of rational functions to...Ch. 1.2 - Use the theorem on limits of rational functions to...Ch. 1.2 - Use the theorem on limits of rational functions to...Ch. 1.2 - For Exercises 19-30, the initial substitution of...Ch. 1.2 - For Exercises 19-30, the initial substitution of ...Ch. 1.2 - For Exercises 19-30, the initial substitution of ...Ch. 1.2 - For Exercises 19-30, the initial substitution of ...Ch. 1.2 - For Exercises 19-30, the initial substitution of...Ch. 1.2 - For Exercises 19-30, the initial substitution of ...Ch. 1.2 - For Exercises 19-30, the initial substitution of ...Ch. 1.2 - For Exercises 19-30, the initial substitution of...Ch. 1.2 - For Exercises 19-30, the initial substitution of...Ch. 1.2 - For Exercises 19-30, the initial substitution of ...Ch. 1.2 - For Exercises 19-30, the initial substitution of...Ch. 1.2 - For Exercises 19-30, the initial substitution of ...Ch. 1.2 - Use the Limit Properties to find the following...Ch. 1.2 - Use the Limit Properties to find the following...Ch. 1.2 - Use the Limit Properties to find the following...Ch. 1.2 - Use the Limit Properties to find the following...Ch. 1.2 - Use the Limit Properties to find the following...Ch. 1.2 - Use the Limit Properties to find the following...Ch. 1.2 - Determine whether each of the function show in...Ch. 1.2 - Determine whether each of the function show in...Ch. 1.2 - Determine whether each of the function show in...Ch. 1.2 - Determine whether each of the function show in...Ch. 1.2 - Determine whether each of the function show in...Ch. 1.2 - Use the graphs and functions in Exercises 37-41 to...Ch. 1.2 - Use the graphs and functions in Exercises 37-41 to...Ch. 1.2 - Use the graphs and functions in Exercises 37-41 to...Ch. 1.2 - Use the graphs and functions in Exercises 37-41 to...Ch. 1.2 - Use the graphs and functions in Exercises 37-41 to...Ch. 1.2 - Answer Exercises 47-48 using the graph...Ch. 1.2 - Answer Exercises 47-48 using the graph...Ch. 1.2 - 49. Is the function given by continuous at ? Why...Ch. 1.2 - Is the function given by f(x)=3x2 continuous at...Ch. 1.2 - Is the function given by G(x)=1x continuous at...Ch. 1.2 - Is the function given by F(x)=x continuous at x=1?...Ch. 1.2 - Is the function given by...Ch. 1.2 - Is the function given by...Ch. 1.2 - Is the function given by...Ch. 1.2 - 56. Is the function given by
Continuous at? Why...Ch. 1.2 - Is the function given by...Ch. 1.2 - Is the function given by...Ch. 1.2 - 59. Is the function given by
Continuous at? Why...Ch. 1.2 - Is the function given by...Ch. 1.2 - Is the function given by...Ch. 1.2 - 62. Is the following given by
Continuous at? Why...Ch. 1.2 - Is the function given by g(x)=1x27x+10 continuous...Ch. 1.2 - 64. Is the function given by continuous at? Why...Ch. 1.2 - Is the function given by G(x)=1x26x+8 continuous...Ch. 1.2 - 66. Is the function given by continuous at? Why...Ch. 1.2 - 67. Is the function given by continuous over the...Ch. 1.2 - 68. Is the function given by continuous over the...Ch. 1.2 - Is the function given by G(x)=1x1 continuous over...Ch. 1.2 - Is the function given by f(x)=1x+3 continuous over...Ch. 1.2 - 71. Is the function given by continuous on?
Ch. 1.2 - 72. Is the function given by continuous on?
Ch. 1.2 - Business and Economics
73. The candy factory sells...Ch. 1.2 - Business and Economics The candy Shoppe charge...Ch. 1.2 - A lab technician controls the temperature T inside...Ch. 1.2 - 76. In Exercises 73, let
Find k such that the...Ch. 1.2 - In Exercises 74, let...Ch. 1.2 - Find each limit, if it exists. If a limit does not...Ch. 1.2 - In Exercises 7986, find each limit. Use TABLE and...Ch. 1.2 - In Exercises 7986, find each limit. Use TABLE and...Ch. 1.2 - In Exercises 7986, find each limit. Use TABLE and...Ch. 1.2 - In Exercises 79–86, find each limit. Use TABLE and...Ch. 1.2 - In Exercises 7986, find each limit. Use TABLE and...Ch. 1.2 - In Exercises 79–86, find each limit. Use TABLE and...Ch. 1.2 - In Exercises 7986, find each limit. Use TABLE and...Ch. 1.2 - In Exercises 79–86, find each limit. Use TABLE and...Ch. 1.3 - For each function in Exercises 1-16, (a) find the...Ch. 1.3 - For each function in Exercises 1-16, (a) find the...Ch. 1.3 - For each function in Exercises 1-16, (a) find the...Ch. 1.3 - For each function in Exercises 1-16, (a) find the...Ch. 1.3 - For each function in Exercises 1-16, (a) find the...Ch. 1.3 - For each function in Exercises 1-16, (a) find the...Ch. 1.3 - For each function in Exercises 1-16, (a) find the...Ch. 1.3 - For each function in Exercises 1-16, (a) find the...Ch. 1.3 - For each function in Exercises 1-16, (a) find the...Ch. 1.3 - For each function in Exercises 1-16, (a) find the...Ch. 1.3 - For each function in Exercises 1-16, (a) find the...Ch. 1.3 - For each function in Exercises 1-16, (a) find the...Ch. 1.3 - For each function in Exercises 1-16, (a) find the...Ch. 1.3 - For each function in Exercises 1-16, (a) find the...Ch. 1.3 - For each function in Exercises 1-16, (a) find the...Ch. 1.3 - For each function in Exercises 1-16, (a) find the...Ch. 1.3 - For Exercises 17-24, use each graph to estimate...Ch. 1.3 - For Exercises 17-24, use each graph to estimate...Ch. 1.3 - For Exercises 17-24, use each graph to estimate...Ch. 1.3 - For Exercises 17-24, use each graph to estimate...Ch. 1.3 - For Exercises 17-24, use each graph to estimate...Ch. 1.3 - For Exercises 17-24, use each graph to estimate...Ch. 1.3 - For Exercises 17-24, use each graph to estimate...Ch. 1.3 - For Exercises 17-24, use each graph to estimate...Ch. 1.3 - 25. Use the following graph to find the average...Ch. 1.3 - 26. Use the following graph to find the average...Ch. 1.3 - 27. Utility. Utility is a type of function that...Ch. 1.3 - 28. Advertising results. The following graph shows...Ch. 1.3 - Prob. 29ECh. 1.3 - 30. Compound interest. The amount of money, in a...Ch. 1.3 - 31. Population change. The population of payton...Ch. 1.3 - Population change. The undergraduate population at...Ch. 1.3 - Total cost. Suppose Fast Trends determines that...Ch. 1.3 - Total revenue. Suppose Fast Trends determines that...Ch. 1.3 - 35. Growth of a baby. The median weights of babies...Ch. 1.3 - 36. Growth of a baby. Use the graph of boys’...Ch. 1.3 - Home range. It has been show that the home range,...Ch. 1.3 - 38. Reader range. The function given by can be...Ch. 1.3 - Memory. The total numbers of words, M(t), that a...Ch. 1.3 - Gas mileage. At the beginning of a trip, the...Ch. 1.3 - Average velocity. In second, an object dropped...Ch. 1.3 - Prob. 42ECh. 1.3 - 43. Population growth. The two curves below...Ch. 1.3 - 44. Business: comparing rate of changes. The...Ch. 1.3 - 45. Rising cost of collage. Like most things, the...Ch. 1.3 - Find the simplified difference quotient for each...Ch. 1.3 - Find the simplified difference quotient for each...Ch. 1.3 - Find the simplified difference quotient for each...Ch. 1.3 - Find the simplified difference quotient for each...Ch. 1.3 - Find the simplified difference quotient for each...Ch. 1.3 - Find the simplified difference quotient for each...Ch. 1.3 - Find the simplified difference quotient for each...Ch. 1.3 - Find the simplified difference quotient for each...Ch. 1.3 - 54. Below are the steps in the simplification of...Ch. 1.3 - For Exercises 55 and 56, find the simplified...Ch. 1.3 - For Exercises 55 and 56, find the simplified...Ch. 1.4 - In Exercises 1-16;
a. a) Graph the...Ch. 1.4 - In Exercises 1-16;
a. a) Graph the...Ch. 1.4 - In Exercises 1-16;
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a. a) Graph the...Ch. 1.4 - a. a) Graph the function. b. b) Draw tangent lines...Ch. 1.4 - a. a) Graph the function. b. b) Draw tangent lines...Ch. 1.4 - a. a) Graph the function. b. b) Draw tangent lines...Ch. 1.4 - a. a) Graph the function. b. b) Draw tangent lines...Ch. 1.4 - a. a) Graph the function. b. b) Draw tangent lines...Ch. 1.4 - a.Graph the function. b.Draw tangent lines to the...Ch. 1.4 - 17. Find an equation of the tangent line to the...Ch. 1.4 - 18. Find an equation of the tangent line to the...Ch. 1.4 - 19. Find an equation of the tangent line to the...Ch. 1.4 - 20. Find an equation of the tangent line to the...Ch. 1.4 - 21. Find an equation of the tangent line to the...Ch. 1.4 - 22. Find an equation of the tangent line to the...Ch. 1.4 - Find f(x) for f(x)=mx+b.Ch. 1.4 - Find f(x) for f(x)=ax2+bx.Ch. 1.4 - For Exercises 25-28, list the graph at which each...Ch. 1.4 - For Exercises 25-28, list the graph at which each...Ch. 1.4 - For Exercises 25-28, list the graph at which each...Ch. 1.4 - For Exercises 25-28, list the graph at which each...Ch. 1.4 - 29. Draw a graph that is continuous, but not...Ch. 1.4 - Draw a graph that is continuous, with no corners,...Ch. 1.4 - 31. Draw a graph that has a horizontal tangent...Ch. 1.4 - Draw a graph that is differentiable and has...Ch. 1.4 - Draw a graph that has horizontal tangent lines at...Ch. 1.4 - Draw a graph that is continuous for all x, with no...Ch. 1.4 - 35. The postage function. Consider the postage in...Ch. 1.4 - 36. The taxicab fare function. Consider the...Ch. 1.4 - The end-of-day values of the Dow Jones Industrial...Ch. 1.4 - The end-of-day values of the Dow Jones Industrial...Ch. 1.4 - 39. Which of the lines in the following graph...Ch. 1.4 - On the following graph, use a colored pencil to...Ch. 1.4 - For Exercises 41-48, Find for the given...Ch. 1.4 - For Exercises 41-48, Find f(x) for the given...Ch. 1.4 - For Exercises 41-48, Find f(x) for the given...Ch. 1.4 - For Exercises 41-48, Find f(x) for the given...Ch. 1.4 - For Exercises 41-48, Find f(x) for the given...Ch. 1.4 - For Exercises 41-48, Find f(x) for the given...Ch. 1.4 - For Exercises 41-48, Find for the given...Ch. 1.4 - For Exercises 41-48, Find f(x) for the given...Ch. 1.4 - 49. Consider the function given by
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a. a) For...Ch. 1.4 - Consider the function k given by k(x)=|x3|+2. a....Ch. 1.4 - 52. Consider the function k given by
.
a. For...Ch. 1.4 - Let f(x)=x2+4x+3x+1=(x+1)(x+3)x+1=x+3. A student...Ch. 1.4 - 54. Let. A student graphs this function, and the...Ch. 1.4 - Let F be a function given by...Ch. 1.4 - Let G be a function given by...Ch. 1.4 - Let H be a function given by...Ch. 1.4 - Use a calculator to check your answer to Exercises...Ch. 1.4 - Prob. 59ECh. 1.4 - Use a calculator to check your answer to Exercises...Ch. 1.4 - Prob. 61ECh. 1.4 - Use a calculator to check your answer to Exercises...Ch. 1.4 - 58-63. Use a calculator to check your answer to...Ch. 1.4 - Business: growth of an investment. A company...Ch. 1.4 - Use a calculate to determine where f(x), does not...Ch. 1.5 - Find dydx. y=x8Ch. 1.5 - Find dydx. y=x7Ch. 1.5 - Find.
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13.
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24.
Ch. 1.5 - Find each derivative.
25.
Ch. 1.5 - Find each derivative. ddx(x3+4x)Ch. 1.5 - Find each derivative.
27.
Ch. 1.5 - Find each derivative. ddx(x34)Ch. 1.5 - Find each derivative. ddx(5x27x+3)Ch. 1.5 - Find each derivative.
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31.
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33.
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35.
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37.
Ch. 1.5 - Find f(x). f(x)=5xx2/3Ch. 1.5 - Find f(x). f(x)=7x14Ch. 1.5 - Find
40.
Ch. 1.5 - Find f(x). f(x)=x3/23Ch. 1.5 - Find
42.
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46.
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48.
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56. If
Ch. 1.5 - 57. Find an equation of the tangent line to the...Ch. 1.5 - Find an equation (in y=mx+b form) of the tangent...Ch. 1.5 - 59. Find an equation of the tangent line to the...Ch. 1.5 - Find an equation of the tangent line to the graph...Ch. 1.5 - For each function, find the point on the graph at...Ch. 1.5 - For each function, find the point on the graph at...Ch. 1.5 - For each function, find the point on the graph at...Ch. 1.5 - For each function, find the point on the graph at...Ch. 1.5 - For each function, find the point on the graph at...Ch. 1.5 - For each function, find the point on the graph at...Ch. 1.5 - For each function, find the point on the graph at...Ch. 1.5 - For each function, find the point on the graph at...Ch. 1.5 - For each function, find the point on the graph at...Ch. 1.5 - For each function, find the point on the graph at...Ch. 1.5 - For each function, find the point on the graph at...Ch. 1.5 - For each function, find the point on the graph at...Ch. 1.5 - For each function, find the point on the graph at...Ch. 1.5 - For each function, find the point on the graph at...Ch. 1.5 - For each function, find the point on the graph at...Ch. 1.5 - For each function, find the point on the graph at...Ch. 1.5 - For each function, find the point on the graph at...Ch. 1.5 - For each function, find the point on the graph at...Ch. 1.5 - For each the function, find the point on the graph...Ch. 1.5 - For each the function, find the point on the graph...Ch. 1.5 - For each the function, find the point on the graph...Ch. 1.5 - For each the function, find the point on the graph...Ch. 1.5 - For each the function, find the point on the graph...Ch. 1.5 - For each the function, find the point on the graph...Ch. 1.5 - 85. Heading wound. The circumference C, in...Ch. 1.5 - 86. Heading wound. The circular area A, in square...Ch. 1.5 - 87. Growth of a baby. The median weight of a boy...Ch. 1.5 - Prob. 88ECh. 1.5 - 89. Heart rate. The equation
can be used to...Ch. 1.5 - Prob. 90ECh. 1.5 - Population growth rate. In t year, the population...Ch. 1.5 - Median age of women at first marriage. The median...Ch. 1.5 - Prob. 93ECh. 1.5 - Super Bowl ticket prices. The of a ticket to the...Ch. 1.5 - For Exercises 95 and 96, find the interval(s) for...Ch. 1.5 - For Exercises 95 and 96, find the interval(s) for...Ch. 1.5 - Find the points on the graph of y=x443x24 at which...Ch. 1.5 - Find the point on the graph of y=2x6x42 at which...Ch. 1.5 - Use the derivative to help explain why f(x)=x5+x3...Ch. 1.5 - Prob. 100ECh. 1.5 - 101. Use the derivative to help explain why ...Ch. 1.5 - Use the derivative to help explain why f(x)=x3+ax...Ch. 1.5 - Find Each function can be different using the...Ch. 1.5 - Prob. 104ECh. 1.5 - Find dy/dx Each function can be different using...Ch. 1.5 - Find dy/dx Each function can be different using...Ch. 1.5 - Find Each function can be different using the...Ch. 1.5 - Find Each function can be different using the...Ch. 1.5 - Find Each function can be different using the...Ch. 1.5 - Find dy/dx Each function can be different using...Ch. 1.5 - When might Leibniz notation be more convenient...Ch. 1.5 - Prob. 112ECh. 1.5 - Prob. 113ECh. 1.5 - Prob. 114ECh. 1.5 - Prob. 115ECh. 1.5 - Prob. 116ECh. 1.5 - Prob. 117ECh. 1.6 - Differentiate two ways; first, by using the...Ch. 1.6 - Differentiate two ways; first, by using the...Ch. 1.6 - Differentiate two ways; first, by using the...Ch. 1.6 - Differentiate two ways; first, by using the...Ch. 1.6 - Differentiate two ways; first, by using the...Ch. 1.6 - Differentiate two ways; first, by using the...Ch. 1.6 - Differentiate two ways; first, by using the...Ch. 1.6 - Differentiate two ways; first, by using the...Ch. 1.6 - Differentiate two ways; first, by using the...Ch. 1.6 - Differentiate two ways; first, by using the...Ch. 1.6 - Differentiate two ways; first, by using the...Ch. 1.6 - Differentiate two ways; first, by using the...Ch. 1.6 - Differentiate two ways; first, by using the...Ch. 1.6 - Differentiate two ways; first, by using the...Ch. 1.6 - Differentiate two ways; first, by using the...Ch. 1.6 - Differentiate two ways; first, by using the...Ch. 1.6 - Differentiate two ways; first, by using the...Ch. 1.6 - Differentiate two ways; first, by using the...Ch. 1.6 - Differentiate two ways; first, by using the...Ch. 1.6 - Differentiate two ways; first, by using the...Ch. 1.6 - Differentiate each function....Ch. 1.6 - Differentiate each function.
22.
Ch. 1.6 - Differentiate each function. y=5x212x3+3Ch. 1.6 - Differentiate each function.
24.
Ch. 1.6 - Differentiate each function.
25.
Ch. 1.6 - Differentiate each function. G(x)=(8x+x)(5x2+3)Ch. 1.6 - Differentiate each function.
27.
Ch. 1.6 - Differentiate each function. f(t)=t5+2t2t4Ch. 1.6 - Differentiate each function. G(x)=(5x4)2Ch. 1.6 - Differentiate each function.
30.
[Hint: ]
Ch. 1.6 - Differentiate each function. y=(x34x)2Ch. 1.6 - Differentiate each function. y=(3x24x+5)2Ch. 1.6 - Differentiate each function....Ch. 1.6 - Differentiate each function.
34.
Ch. 1.6 - Differentiate each function. F(t)=(t+2t)(t23)Ch. 1.6 - Differentiate each function. G(x)=(3t5t2)(t5t)Ch. 1.6 - Differentiate each function. y=x31x2+1+4x3Ch. 1.6 - Differentiate each function. y=x2+1x315x2Ch. 1.6 - Differentiate each function.
39.
Ch. 1.6 - Differentiate each function. y=x+4x35Ch. 1.6 - Differentiate each function. f(x)=x1x+x1Ch. 1.6 - Differentiate each function. f(x)=xx1+1Ch. 1.6 - Differentiate each function. F(t)=1t4Ch. 1.6 - Differentiate each function.
44.
Ch. 1.6 - Differentiate each function. f(x)=3x25xx21Ch. 1.6 - Differentiate each function.
46.
Ch. 1.6 - Differentiate each function. g(x)=t2+3t+5t2+2t+4Ch. 1.6 - Differentiate each function.
48.
Ch. 1.6 - 49. Find an equation of the tangent line to the...Ch. 1.6 - Find an equation of the tangent line to the graph...Ch. 1.6 - 51. Find an equation of the tangent line to the...Ch. 1.6 - Find an equation of the tangent line to the graph...Ch. 1.6 - Average cost. Prestons Leatherworks finds that...Ch. 1.6 - 54. Average cost. Tongue-Tied Sauces, Inc, finds...Ch. 1.6 - Average revenue. Prestons Leatherworks find that...Ch. 1.6 - 56. Average revenue. Tongue-Tied Sauces, Inc,...Ch. 1.6 - Average profit. Use the information in Exercises...Ch. 1.6 - Average profit. Use the information in exercises...Ch. 1.6 - 59. Average profit. Sparkle pottery has determined...Ch. 1.6 - 60. Average profit. Cruzin’ Boards has found that...Ch. 1.6 - Gross domestic produced. The U.S. gross domestic...Ch. 1.6 - Population growth. The population P, in thousands,...Ch. 1.6 - Prob. 63ECh. 1.6 - Differentiate each function.
64. (Hint: Simplify...Ch. 1.6 - Differentiate each function.
65.
Ch. 1.6 - Differentiate each function.
66.
Ch. 1.6 - Differentiate each function. g(x)=(x38)x2+1x21Ch. 1.6 - Differentiate each function. f(t)=(t5+3)t31t3+1Ch. 1.6 - Differentiate each function....Ch. 1.6 - Let f(x)=xx+1 and g(x)=1x+1. a. Compute f(x). b....Ch. 1.6 - 71. Let and .
a. Compute .
b. Compute .
c. c)...Ch. 1.6 - Write a rule for finding the derivative of...Ch. 1.6 - Is the derivative of the reciprocal of f(x) the...Ch. 1.6 - Sensitivity. The reaction R of the body to a dose...Ch. 1.6 - 75. A proof of the Product Rule appears below....Ch. 1.6 - 76. Business. Refer to Exercises 54, 56, and 58....Ch. 1.6 - 77. Business. Refer to Exercises 53, 55, and 58,...Ch. 1.6 - For the function in each of Exercises 78-83, graph...Ch. 1.6 - For the function in each of Exercises 78-83, graph...Ch. 1.6 - For the function in each of Exercises 78-83, graph...Ch. 1.6 - For the function in each of Exercises 78-83, graph...Ch. 1.6 - For the function in each of Exercises 78-83, graph...Ch. 1.6 - For the function in each of Exercises 78-83, graph...Ch. 1.6 - Use a graph to decide which of the following seems...Ch. 1.7 - Differentiate each function.
1. (Check by...Ch. 1.7 - Differentiate each function. y=(2x+1)2 (Check by...Ch. 1.7 - Differentiate each function. y=(7x)55Ch. 1.7 - Differentiate each function.
4.
Ch. 1.7 - Differentiate each function.
5.
Ch. 1.7 - Differentiate each function.
6.
Ch. 1.7 - Differentiate each function. y=3x24Ch. 1.7 - Differentiate each function.
8.
Ch. 1.7 - Differentiate each function.
9.
Ch. 1.7 - Differentiate each function. y=(8x26)40Ch. 1.7 - Differentiate each function.
11.
Ch. 1.7 - Differentiate each function. y=(x+5)7(4x1)10Ch. 1.7 - Differentiate each function. y=1(4x+5)2Ch. 1.7 - Differentiate each function. y=1(3x+8)2Ch. 1.7 - Differentiate each function. y=4x2(7+5x)3Ch. 1.7 - Differentiate each function. y=7x3(49x)5Ch. 1.7 - Differentiate each function. f(x)=(3+x3)5(1+x7)4Ch. 1.7 - Differentiate each function.
18.
Ch. 1.7 - Differentiate each function. f(x)=x2+(200x)2Ch. 1.7 - Differentiate each function. f(x)=x2+(100x)2Ch. 1.7 - Differentiate each function. G(x)=2x13+(4xx)2Ch. 1.7 - Differentiate each function.
22.
Ch. 1.7 - Differentiate each function.
23.
Ch. 1.7 - Differentiate each function.
24.
Ch. 1.7 - Differentiate each function.
25.
Ch. 1.7 - Differentiate each function. g(x)=(3x1)7(2x+1)5Ch. 1.7 - Differentiate each function.
27.
Ch. 1.7 - Differentiate each function. f(x)=x35x+2Ch. 1.7 - Differentiate each function.
29.
Ch. 1.7 - Differentiate each function.
30.
Ch. 1.7 - Differentiate each function.
31.
Ch. 1.7 - Differentiate each function.
32.
Ch. 1.7 - Differentiate each function. g(x)=3+2x5xCh. 1.7 - Differentiate each function. g(x)=4x3+xCh. 1.7 - Differentiate each function. f(x)=(2x33x2+4x+1)100Ch. 1.7 - Differentiate each function. f(x)=(7x4+6x3x)204Ch. 1.7 - Differentiate each function.
37.
Ch. 1.7 - Differentiate each function.
38.
Ch. 1.7 - Differentiate each function. f(x)=x2+xx2xCh. 1.7 - Differentiate each function.
40.
Ch. 1.7 - Differentiate each function. f(x)=(5x4)7(6x+1)3Ch. 1.7 - Differentiate each function.
42.
Ch. 1.7 - Differentiate each function....Ch. 1.7 - Differentiate each function. y=6x2+x3(x46x)3Ch. 1.7 - Find .
45.
Ch. 1.7 - Find .
46.
Ch. 1.7 - Find .
47.
Ch. 1.7 - Find .
48.
Ch. 1.7 - Find dydu,dudx,anddydx. y=(u+1)(u1)andu=x3+1Ch. 1.7 - Find dydu,dudx,anddydx. y=u(u+1)andu=x32xCh. 1.7 - Find dydx for each pair of functions....Ch. 1.7 - Find for each pair of functions.
52.
Ch. 1.7 - Find dydx for each pair of functions....Ch. 1.7 - Find dydx for each pair of functions....Ch. 1.7 - Find dydx for each pair of functions. Find...Ch. 1.7 - Find dydx for each pair of functions. Find...Ch. 1.7 - 57. Find an equation for the tangent line to the...Ch. 1.7 - Find an equation for the tangent line to the graph...Ch. 1.7 - 59. Find an equation for the tangent line to the...Ch. 1.7 - 60. Find an equation for the tangent line to the...Ch. 1.7 - Consider g(x)=(6x+12x5)2. a. Find g(x) using the...Ch. 1.7 - 62. Consider
.
a. Find using the Quotient and...Ch. 1.7 - 63. Let .
Find .
Ch. 1.7 - Let f(u)=u+1u1andg(x)=u=x. Find (fg)(4).Ch. 1.7 - Let f(u)=u3andg(x)=u=1+3x2. Find (fg)(2).Ch. 1.7 - 66. Let .
Find .
Ch. 1.7 - For Exercises 67-70, Use the chain Rule to...Ch. 1.7 - For Exercises 67-70, Use the chain Rule to...Ch. 1.7 - For Exercises 67-70, Use the chain Rule to...Ch. 1.7 - For Exercises 67-70, Use the chain Rule to...Ch. 1.7 - Total revenue. A total-revenue function is given...Ch. 1.7 - Total cost. A total-cost function is given by...Ch. 1.7 - 73. Total profit. Use the total-cost and total...Ch. 1.7 - 74. Total cost. A company determine that its total...Ch. 1.7 - Consumer credit. The total outstanding consumer...Ch. 1.7 - Utility. Utility is a type of function that occurs...Ch. 1.7 - Compound interest. If 1000 is invested at interest...Ch. 1.7 - Compound interest. If 1000 is invested at interest...Ch. 1.7 - 79. Business profit. French’s Electronics is...Ch. 1.7 - Consumer demand. Suppose the demand function for a...Ch. 1.7 - Chemotherapy. The dosage for Carboplatin...Ch. 1.7 - If f(x) is a function, then (f)(x)=f(f(x)) is the...Ch. 1.7 - If f(x) is a function, then (f)(x)=f(f(x)) is the...Ch. 1.7 - If is a function, then is the composition of ...Ch. 1.7 - If f(x) is a function, then (f)(x)=f(f(x)) is the...Ch. 1.7 - Differentiate. y=(2x3)3+1Ch. 1.7 - Differentiate.
87.
Ch. 1.7 - Differentiate. y=(xx1)3Ch. 1.7 - Prob. 89ECh. 1.7 - Differentiate. y=1x21xCh. 1.7 - Differentiate. y=(x2x1x2+1)3Ch. 1.7 - Differentiate.
92.
Ch. 1.7 - Prob. 93ECh. 1.7 - Prob. 94ECh. 1.7 - 95. The Extended Power Rule (for positive integer...Ch. 1.7 - 96. The following is the beginning of an...Ch. 1.7 - For the function in each of Exercises 97 and 98,...Ch. 1.7 - For the function in each of Exercises 97 and 98,...Ch. 1.7 - Prob. 99ECh. 1.7 - Find the derivative of each of the following...Ch. 1.8 - Find .
1.
Ch. 1.8 - Find d2y/dx2. y=x5+9Ch. 1.8 - Find .
3.
Ch. 1.8 - Find .
4.
Ch. 1.8 - Find .
5.
Ch. 1.8 - Find d2y/dx2. y=4x2+3x1Ch. 1.8 - Find d2y/dx2. y=7x+2Ch. 1.8 - Find d2y/dx2. y=6x3Ch. 1.8 - Find .
9.
Ch. 1.8 - Find .
10.
Ch. 1.8 - Find .
11.
Ch. 1.8 - Find d2y/dx2. y=x4Ch. 1.8 - Find f(x). f(x)=x35xCh. 1.8 - Find f(x). f(x)=x4+3xCh. 1.8 - Find .
15.
Ch. 1.8 - Find .
16.
Ch. 1.8 - Find .
17.
Ch. 1.8 - Find f(x). f(x)=4x3Ch. 1.8 - Find .
19.
Ch. 1.8 - Find f(x). f(x)=(x3+2x)6Ch. 1.8 - Find .
21.
Ch. 1.8 - Find f(x). f(x)=(2x23x+1)10Ch. 1.8 - Find .
23.
Ch. 1.8 - Find f(x). f(x)=(x21)23Ch. 1.8 - Find y. y=x3/25xCh. 1.8 - Find y. y=x2/3+4xCh. 1.8 - Find y. y=(x3x)3/4Ch. 1.8 - Find y. y=(x4+x)2/3Ch. 1.8 - Find .
29.
Ch. 1.8 - Find y. y=2x5/4+x1/2Ch. 1.8 - Find y. y=2x3+1x2Ch. 1.8 - Find y. y=3x41xCh. 1.8 - Find y. y=(x2+3)(4x1)Ch. 1.8 - Find y. y=(x2+3)(4x1)Ch. 1.8 - Find y. y=3x+12x3Ch. 1.8 - Find y. y=2x+35x1Ch. 1.8 - For y=x5, find d4y/dx4.Ch. 1.8 - 38. For , find .
Ch. 1.8 - 39. For , find .
Ch. 1.8 - 40. For , find .
Ch. 1.8 - 41. For , find .
Ch. 1.8 - For f(x)=x2x1/2, find f(4)(x).Ch. 1.8 - For g(x)=x43x37x26x+9, find g(6)(x).Ch. 1.8 - 44. For , find .
Ch. 1.8 - Given s(t)=10t2+2t+5, where s(t) is in meters and...Ch. 1.8 - Given s(t)=t3+t where s(t) is in feet and t is in...Ch. 1.8 - 47. Given
,
where is in miles and t is in hours,...Ch. 1.8 - 48. Given
,
where is in meters and t is in...Ch. 1.8 - Free fall. When an object is dropped the distance...Ch. 1.8 - 50. Free fall. (See Exercises 49.) Suppose a...Ch. 1.8 - Free fall. Find the velocity and acceleration of...Ch. 1.8 - 52. Free fall. Find the velocity and acceleration...Ch. 1.8 - 53. The following graph describes a bicycle...Ch. 1.8 - The following graph describes an airplanes...Ch. 1.8 - Sales. The following graph represents the sales,...Ch. 1.8 - Velocity and acceleration. The following graph...Ch. 1.8 - 57. Sales. A company determine that monthly sales...Ch. 1.8 - Sales. Nadias fashions discovers that the number...Ch. 1.8 - Population. The function P(t)=2000t4t+75 gives the...Ch. 1.8 - 60. Medicine. A medication is injected into the...Ch. 1.8 - Prob. 61ECh. 1.8 - Find y for each function. y=12x+1Ch. 1.8 - Find y for each function. y=x+1x1Ch. 1.8 - Find y for each function. y=xx1Ch. 1.8 - For y=xk, find d5y/dx5.Ch. 1.8 - Prob. 66ECh. 1.8 - Prob. 67ECh. 1.8 - Prob. 68ECh. 1.8 - 69. Free fall. On Earth, all free-fall distance...Ch. 1.8 - Free fall. On the moon, all free-fall distance...Ch. 1.8 - 71. Hang time. On Earth, an object travels after ...Ch. 1.8 - Free fall. Skateboarder Danny way free-fell 28 ft...Ch. 1.8 - An object rolls 1 m in 1 min. Below are four...Ch. 1.8 - A bicyclists distance from her starting point is...Ch. 1.8 - Prob. 75ECh. 1.8 - Prob. 76ECh. 1.8 - Prob. 77ECh. 1.8 - Indeterminate Forms and IHopitals Rule, Let f and...Ch. 1.8 - Prob. 79ECh. 1.8 - Prob. 80ECh. 1.8 - Prob. 81ECh. 1.8 - Prob. 82ECh. 1.8 - Indeterminate Forms and IHopitals Rule, Let f and...Ch. 1.8 - Prob. 84ECh. 1.8 - Prob. 85ECh. 1.8 - Prob. 86ECh. 1.8 - Prob. 87ECh. 1.8 - For the distance function in each of Exercises...Ch. 1.8 - For the distance function in each of Exercises...Ch. 1 - Classify each statement as either true or false....Ch. 1 - Classify each statement as either true or false....Ch. 1 - Classify each statement as either true or...Ch. 1 - Classify each statement as either true or...Ch. 1 - Classify each statement as either true or...Ch. 1 - Classify each statement as either true or...Ch. 1 - Classify each statement as either true or...Ch. 1 - Classify each statement as either true or...Ch. 1 - Match each function in column A with the most...Ch. 1 - Match each function in column A with the most...Ch. 1 - Match each function in column A with the most...Ch. 1 - Match each function in column A with the most...Ch. 1 - Match each function in column A with the most...Ch. 1 - Match each function in column A with the most...Ch. 1 - For Exercises 15-17, consider...Ch. 1 - For Exercises 15-17, consider...Ch. 1 - For Exercises 15-17, consider
.
17. Limit...Ch. 1 - Find each limit, if it exists. If a limit does not...Ch. 1 - Find each limit, if it exists. If a limit does not...Ch. 1 - Find each limit, if it exists. If a limit does not...Ch. 1 - Find each limit, if it exists. If a limit does not...Ch. 1 - For Exercises 22-30, consider the function g...Ch. 1 - For Exercises 22-30, consider the function g...Ch. 1 - For Exercises 22-30, consider the function g...Ch. 1 - For Exercises 22-30, consider the function g...Ch. 1 - For Exercises 22-30, consider the function g...Ch. 1 - For Exercises 22-30, consider the function g...Ch. 1 - For Exercises 22-30, consider the function g...Ch. 1 - For Exercises 22-30, consider the function g...Ch. 1 - For Exercises 22-30, consider the function g...Ch. 1 - For Exercises 31-34, consider the function f...Ch. 1 - For Exercises 31-34, consider the function f...Ch. 1 - For Exercises 31-34, consider the function f...Ch. 1 - For Exercises 31-34, consider the function f...Ch. 1 - 35. For find the average rate of change as x...Ch. 1 - Find a simplified difference quotient for...Ch. 1 - 37. Find a simplify difference quotient for
.
Ch. 1 - 38. Find an equation of the tangent line to the...Ch. 1 - 39. Find the point(s) on the graph of at which...Ch. 1 - 40. Find the point(s) on the graph of at which...Ch. 1 - Find .
41.
Ch. 1 - Find dy/dx. y=8x3 [1.5]Ch. 1 - Find .
43.
Ch. 1 - Find dy/dx. y=15x2/5 [1.5]Ch. 1 - Find .
45.
Ch. 1 - Differentiate. f(x)=512x6+8x42x [1.5]Ch. 1 - Differentiate.
47.
Ch. 1 - Differentiate. y=x2+88x [1.6]Ch. 1 - Differentiate.
49.
Ch. 1 - Differentiate. f(x)=(x53)7 [1.7]Ch. 1 - Differentiate. f(x)=x2(4x+2)3/4 [1.7]Ch. 1 - 52. For .
Ch. 1 - For y=342x710x3+13x2+28x2,findy. [1.8]Ch. 1 - 54. Social science: growth rate. The population of...Ch. 1 - For Exercises 55-58, consider the growth of , the...Ch. 1 - For Exercises 55-58, consider the growth of , the...Ch. 1 - For Exercises 55-58, consider the growth of...Ch. 1 - For Exercises 55-58, consider the growth of...Ch. 1 - For s(t)=t+t4, with t in seconds and s(t) in feet,...Ch. 1 - Business: average revenue, cost, and profit. Given...Ch. 1 - Find ddx(fg)(x) and ddx(gf)(x), given f(x)=x2+5...Ch. 1 - Prob. 62RECh. 1 - Prob. 63RECh. 1 - Prob. 64RECh. 1 - Prob. 65RECh. 1 - Prob. 66RECh. 1 - For Exercises 1-3, consider
,
1. Numerical...Ch. 1 - For Exercises 1-3, consider...Ch. 1 - For Exercises 1-3, consider...Ch. 1 - For Exercises 4-15, consider the function f...Ch. 1 - For Exercises 4-15, consider the function f...Ch. 1 - For Exercises 4-15, consider the function f...Ch. 1 - For Exercises 4-15, consider the function f...Ch. 1 - For Exercises 4-15, consider the function f...Ch. 1 - For Exercises 4-15, consider the function f...Ch. 1 - For Exercises 4-15, consider the function f...Ch. 1 - For Exercises 4-15, consider the function f...Ch. 1 - For Exercises 4-15, consider the function f...Ch. 1 - For Exercises 4-15, consider the function f...Ch. 1 - For Exercises 4-15, consider the function f...Ch. 1 - For Exercises 4-15, consider the function f...Ch. 1 - Determine whether each function is continuous. If...Ch. 1 - Determine whether each function is continuous. If...Ch. 1 - For Exercises 18 and 19, consider the function...Ch. 1 - For Exercises 18 and 19, consider the function...Ch. 1 - Find each limit, if it exists. If a limit does not...Ch. 1 - Find each limit, if it exists. If a limit does not...Ch. 1 - Find each limit, if it exists. If a limit does not...Ch. 1 - Find the simplified difference quotient for...Ch. 1 - Find an equation of the line tangent to y=x+(4/x)...Ch. 1 - 25. Find the point(s) on the graph of at which...Ch. 1 - Find dy/dx y=x23Ch. 1 - Find
27.
Ch. 1 - Find dy/dx y=10xCh. 1 - Find dy/dx y=x5/4Ch. 1 - Find dy/dx y=0.5x2+0.61x+90Ch. 1 - Differentiate y=13x3x2+2x+4Ch. 1 - Differentiate
32.
Ch. 1 - Differentiate f(x)=x5xCh. 1 - Differentiate f(x)=(x+3)4(7x)5Ch. 1 - Differentiate y=(x54x3+x)5Ch. 1 - Differentiate
36.
Ch. 1 - Differentiate For y=x43x2 find d3ydx3.Ch. 1 - 38. Social science: memory. In a certain memory...Ch. 1 - Business: average revenue, cost, and profit. Given...Ch. 1 - For Exercises 40 and 41, let and .
40. Find
Ch. 1 - For Exercises 40 and 41, let f(x)=x2x and...Ch. 1 - A ball is placed on an inclined plane and, due to...Ch. 1 - Prob. 43TCh. 1 - Find limx3x327x3.Ch. 1 - Prob. 45TCh. 1 - Find the following limit by creating a table of...Ch. 1 - Plot the points and connect them with line...Ch. 1 - 2. a. a) Use REGRESSION to find a cubic...Ch. 1 - 3. a. a) Use REGRESSION to find a quartic...Ch. 1 - a. a) Although most calculate cannot fit such a...Ch. 1 - Prob. 5ETECh. 1 - Prob. 6ETECh. 1 - Prob. 7ETECh. 1 - Prob. 8ETE
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- f'(x)arrow_forwardA body of mass m at the top of a 100 m high tower is thrown vertically upward with an initial velocity of 10 m/s. Assume that the air resistance FD acting on the body is proportional to the velocity V, so that FD=kV. Taking g = 9.75 m/s2 and k/m = 5 s, determine: a) what height the body will reach at the top of the tower, b) how long it will take the body to touch the ground, and c) the velocity of the body when it touches the ground.arrow_forwardA chemical reaction involving the interaction of two substances A and B to form a new compound X is called a second order reaction. In such cases it is observed that the rate of reaction (or the rate at which the new compound is formed) is proportional to the product of the remaining amounts of the two original substances. If a molecule of A and a molecule of B combine to form a molecule of X (i.e., the reaction equation is A + B ⮕ X), then the differential equation describing this specific reaction can be expressed as: dx/dt = k(a-x)(b-x) where k is a positive constant, a and b are the initial concentrations of the reactants A and B, respectively, and x(t) is the concentration of the new compound at any time t. Assuming that no amount of compound X is present at the start, obtain a relationship for x(t). What happens when t ⮕∞?arrow_forwardConsider a body of mass m dropped from rest at t = 0. The body falls under the influence of gravity, and the air resistance FD opposing the motion is assumed to be proportional to the square of the velocity, so that FD = kV2. Call x the vertical distance and take the positive direction of the x-axis downward, with origin at the initial position of the body. Obtain relationships for the velocity and position of the body as a function of time t.arrow_forwardAssuming that the rate of change of the price P of a certain commodity is proportional to the difference between demand D and supply S at any time t, the differential equations describing the price fluctuations with respect to time can be expressed as: dP/dt = k(D - s) where k is the proportionality constant whose value depends on the specific commodity. Solve the above differential equation by expressing supply and demand as simply linear functions of price in the form S = aP - b and D = e - fParrow_forwardFind the area of the surface obtained by rotating the circle x² + y² = r² about the line y = r.arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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