CALCULUS+ITS APPLICATIONS
CALCULUS+ITS APPLICATIONS
12th Edition
ISBN: 9780135164884
Author: BITTINGER
Publisher: PEARSON
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Concept explainers

Rate of Change
The relation between two quantities which displays how much greater one quantity is than another is called ratio.
Slope
The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:
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Textbook Question
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Chapter 1.4, Problem 15E

a.Graph the function.

b.Draw tangent lines to the graph at point whose x-coordinates are –2, 0, and 1.

c.Find f ' ( x ) by determining lim x → 0 f ( x + h ) − f ( x ) h .

d. d) Find f ' ( − 2 ) , f ' ( 0 , )       and       f ' ( 1 ) . These slopes should match those of the lines you drew in part (b).

f ( x ) = 2 x

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Chapter 1 Solutions

CALCULUS+ITS APPLICATIONS

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. 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 - 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 - 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 25-32, 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 25-32, 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 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 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 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 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 61-78, graph each function and then...Ch. 1.1 - Prob. 66ECh. 1.1 - For Exercises 61-78, graph each function and then...Ch. 1.1 - Prob. 68ECh. 1.1 - For Exercises 61-78, graph each function and then...Ch. 1.1 - Prob. 70ECh. 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 - Prob. 82ECh. 1.1 - Prob. 83ECh. 1.1 - Prob. 84ECh. 1.1 - Prob. 85ECh. 1.1 - Prob. 86ECh. 1.1 - Tax rate schedule. The federal tax rate for single...Ch. 1.1 - Prob. 88ECh. 1.1 - Prob. 89ECh. 1.1 - Prob. 90ECh. 1.1 - Prob. 91ECh. 1.1 - Prob. 92ECh. 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 - Prob. 96ECh. 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 - Prob. 1ECh. 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...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 - Prob. 31ECh. 1.2 - Use the Limit Properties to find the following...Ch. 1.2 - Prob. 33ECh. 1.2 - Use the Limit Properties to find the following...Ch. 1.2 - Prob. 35ECh. 1.2 - Use the Limit Properties to find the following...Ch. 1.2 - Prob. 37ECh. 1.2 - Use the Limit Properties to find the following...Ch. 1.2 - Prob. 39ECh. 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 - 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 - Prob. 65ECh. 1.2 - 56. Is the function given by Continuous at? Why...Ch. 1.2 - Is the function given by...Ch. 1.2 - Prob. 68ECh. 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 - Prob. 79ECh. 1.2 - Prob. 80ECh. 1.2 - Prob. 81ECh. 1.2 - Prob. 82ECh. 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 - Prob. 86ECh. 1.2 - Prob. 87ECh. 1.2 - Prob. 88ECh. 1.2 - Prob. 89ECh. 1.2 - Prob. 90ECh. 1.2 - Prob. 91ECh. 1.2 - Prob. 92ECh. 1.2 - Prob. 93ECh. 1.2 - Prob. 94ECh. 1.2 - Prob. 95ECh. 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 - In Exercises 1-10, state the average rate of...Ch. 1.3 - In Exercises 1-10, state the average rate of...Ch. 1.3 - In Exercises 110, state the average rate of change...Ch. 1.3 - Prob. 4ECh. 1.3 - Prob. 5ECh. 1.3 - Prob. 6ECh. 1.3 - Prob. 7ECh. 1.3 - Prob. 8ECh. 1.3 - In Exercises 1-10, state the average rate of...Ch. 1.3 - Prob. 10ECh. 1.3 - In Exercises 11-20, find the average rate of...Ch. 1.3 - In Exercises 11-20, find the average rate of...Ch. 1.3 - Prob. 13ECh. 1.3 - In Exercises 11-20, find the average rate of...Ch. 1.3 - In Exercises 11-20, find the average rate of...Ch. 1.3 - In Exercises 11-20, find the average rate of...Ch. 1.3 - Prob. 17ECh. 1.3 - In Exercises 11-20, find the average rate of...Ch. 1.3 - In Exercises 11-20, find the average rate of...Ch. 1.3 - In Exercises 11-20, find the average rate of...Ch. 1.3 - Prob. 21ECh. 1.3 - For each function in Exercises 21-36, (a) find the...Ch. 1.3 - Prob. 23ECh. 1.3 - For each function in Exercises 21-36, (a) find the...Ch. 1.3 - Prob. 25ECh. 1.3 - For each function in Exercises 21-36, (a) find the...Ch. 1.3 - For each function in Exercises 21-36, (a) find the...Ch. 1.3 - For each function in Exercises 21-36, (a) find the...Ch. 1.3 - Prob. 29ECh. 1.3 - For each function in Exercises 21-36, (a) find the...Ch. 1.3 - Prob. 31ECh. 1.3 - For each function in Exercises 21-36, (a) find the...Ch. 1.3 - Prob. 33ECh. 1.3 - For each function in Exercises 21-36, (a) find the...Ch. 1.3 - Prob. 35ECh. 1.3 - For each function in Exercises 21-36, (a) find the...Ch. 1.3 - For Exercises 37-44, use each graph to estimate...Ch. 1.3 - For Exercises 37-44, use each graph to estimate...Ch. 1.3 - Prob. 39ECh. 1.3 - For Exercises 37-44, use each graph to estimate...Ch. 1.3 - For Exercises 37-44, use each graph to estimate...Ch. 1.3 - For Exercises 37-44, use each graph to estimate...Ch. 1.3 - Prob. 43ECh. 1.3 - For Exercises 37-44, use each graph to estimate...Ch. 1.3 - Prob. 45ECh. 1.3 - Use the following graph to find the average rate...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 - Total cost. Suppose Fast Trends determines that...Ch. 1.3 - Total revenue. Suppose Fast Trends determines that...Ch. 1.3 - Home range. It has been show that the home range,...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. 60ECh. 1.3 - 43. Population growth. The two curves below...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 - 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 - a.Graph the function. b.Draw tangent lines to the...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; a. a) Graph the...Ch. 1.4 - a.Graph the function. b.Draw tangent lines to the...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 - a.Graph the function. b.Draw tangent lines to 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.Graph the function. b.Draw tangent lines to the...Ch. 1.4 - a. a) Graph the function. b. b) Draw tangent lines...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 - 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 - Prob. 38ECh. 1.4 - In Exercises 39-42, classify each statement as...Ch. 1.4 - Prob. 40ECh. 1.4 - Prob. 42ECh. 1.4 - Prob. 43ECh. 1.4 - For Exercises 45-51, find f(x) for the given...Ch. 1.4 - Prob. 46ECh. 1.4 - Prob. 47ECh. 1.4 - Prob. 48ECh. 1.4 - For Exercises 45-51, find f(x) for the given...Ch. 1.4 - Prob. 50ECh. 1.4 - Prob. 51ECh. 1.4 - Prob. 52ECh. 1.4 - Prob. 53ECh. 1.4 - Prob. 54ECh. 1.4 - Prob. 55ECh. 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 - Prob. 64ECh. 1.5 - For the function given by u=f(v), write four...Ch. 1.5 - Prob. 2ECh. 1.5 - Prob. 3ECh. 1.5 - Prob. 4ECh. 1.5 - For the function given by h=m(k), write four...Ch. 1.5 - Prob. 6ECh. 1.5 - Find dydx. y=x7Ch. 1.5 - Find dydx. y=x8Ch. 1.5 - Find. 4. Ch. 1.5 - Find. 3. Ch. 1.5 - Find. 6. Ch. 1.5 - Find. 5. Ch. 1.5 - Find. 8. Ch. 1.5 - Find. 7. Ch. 1.5 - Find dydx. y=x6Ch. 1.5 - Find. 9. Ch. 1.5 - Find. 12. Ch. 1.5 - Find dydx. y=3x5Ch. 1.5 - Find dydx. y=x3+3x2Ch. 1.5 - Find. 13. Ch. 1.5 - Find. 16. Ch. 1.5 - Find. 15. Ch. 1.5 - Find. 18. Ch. 1.5 - Prob. 24ECh. 1.5 - Find. 20. Ch. 1.5 - Find. 19. Ch. 1.5 - Find. 22. Ch. 1.5 - Find. 21. 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 - Prob. 33ECh. 1.5 - Prob. 34ECh. 1.5 - Find each derivative. 35. f(x)=25x6Ch. 1.5 - Prob. 36ECh. 1.5 - Find each derivative. 37. f(x)=4xx3/5Ch. 1.5 - Prob. 38ECh. 1.5 - Find g(x). 39. g(x)=7x14Ch. 1.5 - Prob. 40ECh. 1.5 - Find g(x). 41. g(x)=x3/23Ch. 1.5 - Prob. 42ECh. 1.5 - Find f(x). f(x)=0.01x2+0.4x+500.02x+0.4Ch. 1.5 - Find f(x). f(x)=0.01x20.5x+700.02x0.5Ch. 1.5 - Find y y=x3/43x2/3+x5/4+2x434x7/42x1/3+54x1/48x5Ch. 1.5 - Find 46. Ch. 1.5 - Find y y=x7+7xCh. 1.5 - Find 48. Ch. 1.5 - Find y If f(x)=x,findf(4).Ch. 1.5 - Find 50. If. Ch. 1.5 - If y=x+2x3, find dydx at x=1.Ch. 1.5 - If y=4x2, find dydx at x=2.Ch. 1.5 - If y=x3+x, find dydx at x=64.Ch. 1.5 - Prob. 54ECh. 1.5 - If y=25x3, find dydx at x=4.Ch. 1.5 - Prob. 56ECh. 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 - Prob. 85ECh. 1.5 - Prob. 86ECh. 1.5 - Growth of a child. The median weight of a boy...Ch. 1.5 - Prob. 88ECh. 1.5 - Prob. 90ECh. 1.5 - Population growth rate. In t year, the population...Ch. 1.5 - Prob. 93ECh. 1.5 - Prob. 94ECh. 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 - 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. 105ECh. 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 - Prob. 113ECh. 1.5 - Prob. 114ECh. 1.5 - Prob. 115ECh. 1.5 - Prob. 116ECh. 1.5 - Prob. 117ECh. 1.5 - Prob. 118ECh. 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. 22. Ch. 1.6 - Differentiate each function....Ch. 1.6 - Differentiate each function. y=5x212x3+3Ch. 1.6 - Differentiate each function. 24. Ch. 1.6 - Differentiate each function. G(x)=(8x+x)(5x2+3)Ch. 1.6 - Differentiate each function. 25. Ch. 1.6 - Differentiate each function. 27. Ch. 1.6 - Differentiate each function. f(t)=t5+2t2t4Ch. 1.6 - Differentiate each function. 30. [Hint: ] Ch. 1.6 - Differentiate each function. G(x)=(5x4)2Ch. 1.6 - Differentiate each function. y=(x34x)2Ch. 1.6 - Differentiate each function. y=(3x24x+5)2Ch. 1.6 - Differentiate each function. 34. Ch. 1.6 - Differentiate each function....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=x2+1x315x2Ch. 1.6 - Differentiate each function. y=x31x2+1+4x3Ch. 1.6 - Differentiate each function. 39. Ch. 1.6 - Differentiate each function. y=x+4x35Ch. 1.6 - Differentiate each function. f(x)=xx1+1Ch. 1.6 - Differentiate each function. f(x)=x1x+x1Ch. 1.6 - Differentiate each function. F(t)=1t4Ch. 1.6 - Differentiate each function. 44. Ch. 1.6 - Differentiate each function. 46. Ch. 1.6 - Differentiate each function. f(x)=3x25xx21Ch. 1.6 - Differentiate each function. g(x)=t2+3t+5t2+2t+4Ch. 1.6 - Differentiate each function. 48. Ch. 1.6 - Find an equation of the tangent line to the graph...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 - 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 - Prob. 61ECh. 1.6 - Temperature during an illness. Ginas temperature T...Ch. 1.6 - Prob. 63ECh. 1.6 - Prob. 64ECh. 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 - 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 - Prob. 76ECh. 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 - Prob. 81ECh. 1.7 - Differentiate each function using the Chain Rule....Ch. 1.7 - Prob. 2ECh. 1.7 - Prob. 3ECh. 1.7 - Prob. 4ECh. 1.7 - Differentiate each function using the Chain Rule....Ch. 1.7 - Prob. 6ECh. 1.7 - Prob. 7ECh. 1.7 - Prob. 8ECh. 1.7 - Differentiate each function using the Chain Rule....Ch. 1.7 - Prob. 10ECh. 1.7 - Differentiate each function using the Chain Rule....Ch. 1.7 - Prob. 12ECh. 1.7 - Prob. 13ECh. 1.7 - Differentiate each function using the Chain Rule....Ch. 1.7 - Differentiate each function using the Chain Rule....Ch. 1.7 - Prob. 16ECh. 1.7 - Prob. 17ECh. 1.7 - Prob. 18ECh. 1.7 - Prob. 19ECh. 1.7 - Differentiate each function using the Chain Rule....Ch. 1.7 - Differentiate each function using the Chain Rule....Ch. 1.7 - Prob. 22ECh. 1.7 - Prob. 23ECh. 1.7 - Differentiate each function using the Chain Rule....Ch. 1.7 - Differentiate each function using the Chain Rule....Ch. 1.7 - Prob. 26ECh. 1.7 - Prob. 27ECh. 1.7 - Prob. 28ECh. 1.7 - Prob. 29ECh. 1.7 - Prob. 30ECh. 1.7 - Differentiate each function using the Chain Rule....Ch. 1.7 - Prob. 32ECh. 1.7 - Find . 45. Ch. 1.7 - Prob. 34ECh. 1.7 - Find . 47. Ch. 1.7 - Find . 48. Ch. 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. Find...Ch. 1.7 - Prob. 40ECh. 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 - Let h(x)=3x2+2x5. Find functions f and g such that...Ch. 1.7 - Prob. 52ECh. 1.7 - Prob. 53ECh. 1.7 - Prob. 54ECh. 1.7 - Prob. 55ECh. 1.7 - Prob. 56ECh. 1.7 - Prob. 57ECh. 1.7 - Prob. 58ECh. 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 - Total profit. Use the total-cost and total-revenue...Ch. 1.7 - Total cost. Solid Seats, Inc., determines that its...Ch. 1.7 - Compound interest. If 1000 is invested at interest...Ch. 1.7 - Prob. 64ECh. 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 - Prob. 68ECh. 1.7 - Prob. 69ECh. 1.7 - Prob. 70ECh. 1.7 - Prob. 71ECh. 1.7 - Prob. 72ECh. 1.7 - Prob. 73ECh. 1.7 - Prob. 74ECh. 1.7 - Differentiate. 87. Ch. 1.7 - Prob. 76ECh. 1.7 - Differentiate. y=1x21xCh. 1.7 - Differentiate. y=(x2x1x2+1)3Ch. 1.7 - Differentiate. 92. Ch. 1.7 - Prob. 80ECh. 1.7 - Prob. 81ECh. 1.7 - Prob. 82ECh. 1.7 - Prob. 83ECh. 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. 1.8 - Find d2y/dx2. y=x5+9Ch. 1.8 - Find . 1. Ch. 1.8 - Find . 4. Ch. 1.8 - Find . 3. Ch. 1.8 - Find d2y/dx2. y=4x2+3x1Ch. 1.8 - Find . 5. Ch. 1.8 - Find d2y/dx2. y=6x3Ch. 1.8 - Find d2y/dx2. y=7x+2Ch. 1.8 - Find . 10. Ch. 1.8 - Find . 9. Ch. 1.8 - Find d2y/dx2. y=x4Ch. 1.8 - Find . 11. Ch. 1.8 - Find f(x). f(x)=x4+3xCh. 1.8 - Find f(x). f(x)=x35xCh. 1.8 - Find . 16. Ch. 1.8 - Find . 15. Ch. 1.8 - Find f(x). f(x)=4x3Ch. 1.8 - Find . 17. Ch. 1.8 - Find f(x). f(x)=(x3+2x)6Ch. 1.8 - Find . 19. Ch. 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 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 - Given s(t)=t3+t where s(t) is in feet and t is in...Ch. 1.8 - Given s(t)=10t2+2t+5, where s(t) is in meters and...Ch. 1.8 - 48. Given , where is in meters and t is in...Ch. 1.8 - 47. Given , where is in miles and t is in hours,...Ch. 1.8 - Free fall. When an object is dropped the distance...Ch. 1.8 - Prob. 40ECh. 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. 51ECh. 1.8 - Prob. 52ECh. 1.8 - Prob. 53ECh. 1.8 - Prob. 54ECh. 1.8 - Prob. 55ECh. 1.8 - Prob. 56ECh. 1.8 - Prob. 57ECh. 1.8 - Prob. 58ECh. 1.8 - Prob. 59ECh. 1.8 - Prob. 60ECh. 1.8 - Prob. 61ECh. 1.8 - Prob. 62ECh. 1.8 - Free fall. On the moon, all free-fall distance...Ch. 1.8 - Prob. 64ECh. 1.8 - Prob. 65ECh. 1.8 - A bicyclists distance from her starting point is...Ch. 1.8 - Prob. 67ECh. 1.8 - Prob. 68ECh. 1.8 - Prob. 69ECh. 1.8 - Prob. 70ECh. 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 - Prob. 22RECh. 1 - Prob. 23RECh. 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 - 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 - Prob. 56RECh. 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 - Prob. 61RECh. 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. 64RECh. 1 - Prob. 65RECh. 1 - Prob. 66RECh. 1 - Prob. 67RECh. 1 - Prob. 68RECh. 1 - For Exercises 1-3, consider , 1. Numerical...Ch. 1 - For Exercises 1-3, consider...Ch. 1 - For Exercises 1-3, consider...Ch. 1 - Graphical limits. For Exercises 4-15, consider the...Ch. 1 - Prob. 5TCh. 1 - Prob. 6TCh. 1 - Prob. 7TCh. 1 - Prob. 8TCh. 1 - Prob. 9TCh. 1 - Prob. 10TCh. 1 - Prob. 11TCh. 1 - Graphical limits. For Exercises 4-15, consider the...Ch. 1 - Prob. 13TCh. 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 - Prob. 6ETECh. 1 - Prob. 7ETECh. 1 - Prob. 8ETE

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Differential Equation | MIT 18.01SC Single Variable Calculus, Fall 2010; Author: MIT OpenCourseWare;https://www.youtube.com/watch?v=HaOHUfymsuk;License: Standard YouTube License, CC-BY