MYMATHLAB ACCESS CODE - MATHEMATICS WIT
12th Edition
ISBN: 9780135904282
Author: Lial, HUNGERFO
Publisher: PEARSON
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Chapter 12.6, Problem 2E
To determine
To graph: The function
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4. Direction Fields/Phase Portraits. Use the given direction fields to plot solution curves
to each of the given initial value problems.
(a)
x = x+2y
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y = -3x+y
with x(0) = 1, y(0) = -1
(b) Consider the initial value problem corresponding to the given phase portrait.
x = y
y' = 3x + 2y
Draw two "straight line solutions"
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Chapter 12 Solutions
MYMATHLAB ACCESS CODE - MATHEMATICS WIT
Ch. 12.1 - Checkpoint 1
For what values of x is the function...Ch. 12.1 - Checkpoint 2
Find all intervals on which is...Ch. 12.1 - Checkpoint 3
Identity the x-values of all points...Ch. 12.1 - Checkpoint 4
Find the critical numbers for each of...Ch. 12.1 - Prob. 5CPCh. 12.1 - Prob. 6CPCh. 12.1 - Checkpoint 7 Find the locations of the local...Ch. 12.1 - Prob. 8CPCh. 12.1 - Checkpoint 9
If a sales function is given by...Ch. 12.1 - Prob. 1E
Ch. 12.1 - Prob. 2ECh. 12.1 - Prob. 3ECh. 12.1 - Prob. 4ECh. 12.1 - Prob. 5ECh. 12.1 - Prob. 6ECh. 12.1 - Prob. 7ECh. 12.1 - Prob. 8ECh. 12.1 - Find the intervals on which each function is...Ch. 12.1 - Find the intervals on which each function is...Ch. 12.1 - Prob. 13ECh. 12.1 - Prob. 12ECh. 12.1 - Prob. 15ECh. 12.1 - Find the intervals on which each function is...Ch. 12.1 - Find the intervals on which each function is...Ch. 12.1 - Find the intervals on which each function is...Ch. 12.1 - Prob. 11ECh. 12.1 - Prob. 14ECh. 12.1 - Prob. 19ECh. 12.1 - Prob. 20ECh. 12.1 - Prob. 21ECh. 12.1 - Determine the location of each local extremum of...Ch. 12.1 - Prob. 23ECh. 12.1 - Prob. 24ECh. 12.1 - Prob. 25ECh. 12.1 - Prob. 26ECh. 12.1 - Determine the location of each local extremum of...Ch. 12.1 - Determine the location of each local extremum of...Ch. 12.1 - Prob. 29ECh. 12.1 - Prob. 30ECh. 12.1 - Determine the location of each local extremum of...Ch. 12.1 - Prob. 32ECh. 12.1 - In Exercises 29–40, use the first-derivative test...Ch. 12.1 - In Exercises 29–40, use the first-derivative test...Ch. 12.1 - In Exercises 29–40, use the first-derivative test...Ch. 12.1 - Prob. 36ECh. 12.1 - Prob. 37ECh. 12.1 - Prob. 38ECh. 12.1 - Prob. 39ECh. 12.1 - Prob. 40ECh. 12.1 - Use the maximum/minimum finder on a graphing...Ch. 12.1 - Prob. 42ECh. 12.1 - Prob. 43ECh. 12.1 - Prob. 44ECh. 12.1 - Work the given exercises. (See Examples 1 and...Ch. 12.1 - Prob. 46ECh. 12.1 - Prob. 48ECh. 12.1 - Prob. 47ECh. 12.1 - Work the given exercises. (See Examples 5 and 9.)...Ch. 12.1 - Prob. 50ECh. 12.1 - Prob. 51ECh. 12.1 - 51. Physical Science A Boston Red Sox pitcher...Ch. 12.1 - Prob. 52ECh. 12.1 - Work the given exercises. (See Examples 5 and 9.)...Ch. 12.1 - Prob. 55ECh. 12.1 - Work these exercises. You may need to use the...Ch. 12.1 - Prob. 56ECh. 12.1 - Work these exercises. (See Examples 5 and 9.)...Ch. 12.1 - Work these exercises. (See Examples 5 and 9.) IBM...Ch. 12.1 - Work these exercises. You may need to use the...Ch. 12.1 - Work these exercises. You may need to use the...Ch. 12.1 - Prob. 62ECh. 12.1 - Prob. 63ECh. 12.1 - Prob. 64ECh. 12.1 - 65. Social Science A group of researchers found...Ch. 12.1 - Prob. 66ECh. 12.1 - Prob. 68ECh. 12.1 - Prob. 67ECh. 12.1 - Prob. 69ECh. 12.1 - Prob. 70ECh. 12.2 - Checkpoint 1 Let f(x)=x35x27x+99. Find f(x); f(x);...Ch. 12.2 - Prob. 2CPCh. 12.2 - Prob. 3CPCh. 12.2 - Prob. 4CPCh. 12.2 - Prob. 5CPCh. 12.2 - Prob. 6CPCh. 12.2 - For each of these functions, find and (See...Ch. 12.2 - For each of these functions, find and (See...Ch. 12.2 - Prob. 3ECh. 12.2 - For each of these functions, find and (See...Ch. 12.2 - For each of these functions, find and (See...Ch. 12.2 - Prob. 15ECh. 12.2 - Prob. 16ECh. 12.2 - For each of these functions, find and (See...Ch. 12.2 - For each of these functions, find and (See...Ch. 12.2 - For each of these functions, find . (See Examples...Ch. 12.2 - For each of these functions, find and (See...Ch. 12.2 - For each of these functions, find and (See...Ch. 12.2 - For each of these functions, find and (See...Ch. 12.2 - For each of these functions, find and (See...Ch. 12.2 - For each of these functions, find and (See...Ch. 12.2 - For each of these functions, find and (See...Ch. 12.2 - For each of these functions, find and (See...Ch. 12.2 - For each of these functions, find and (See...Ch. 12.2 - In Exercises 19 and 20, P(t) is the price of a...Ch. 12.2 - In Exercise 19 and 20, is the price of a certain...Ch. 12.2 - Physical Science Each of the functions in...Ch. 12.2 - Physical Science Each of the functions in...Ch. 12.2 - Prob. 23ECh. 12.2 - Prob. 24ECh. 12.2 - Prob. 25ECh. 12.2 - Prob. 26ECh. 12.2 - Find the largest open intervals on which each...Ch. 12.2 - Prob. 28ECh. 12.2 - Find the largest open intervals on which each...Ch. 12.2 - Find the largest open intervals on which each...Ch. 12.2 - Find the largest open intervals on which each...Ch. 12.2 - Find the largest open intervals on which each...Ch. 12.2 - Prob. 33ECh. 12.2 - Prob. 34ECh. 12.2 - Business In Exercises 33–36, find the point of...Ch. 12.2 - Business In Exercises 33–36, find the point of...Ch. 12.2 - Find all critical numbers of the functions in...Ch. 12.2 - Find all critical numbers of the functions in...Ch. 12.2 - Find all critical numbers of the functions in...Ch. 12.2 - Prob. 40ECh. 12.2 - Prob. 41ECh. 12.2 - Prob. 42ECh. 12.2 - Prob. 43ECh. 12.2 - Prob. 44ECh. 12.2 - Prob. 45ECh. 12.2 - Find all critical numbers of the functions in...Ch. 12.2 - Prob. 47ECh. 12.2 - Prob. 48ECh. 12.2 - Prob. 51ECh. 12.2 - Prob. 52ECh. 12.2 - Prob. 49ECh. 12.2 - Prob. 50ECh. 12.2 - Prob. 56ECh. 12.2 - Prob. 53ECh. 12.2 - Prob. 54ECh. 12.2 - Prob. 55ECh. 12.2 - Prob. 57ECh. 12.2 - Prob. 58ECh. 12.2 - Prob. 59ECh. 12.2 - Prob. 60ECh. 12.2 - Prob. 61ECh. 12.2 - Prob. 62ECh. 12.2 - 65. Social Science The population of Wyoming (in...Ch. 12.2 - Prob. 65ECh. 12.2 - Prob. 66ECh. 12.3 - Checkpoint 1
Find the location of the absolute...Ch. 12.3 - Prob. 2CPCh. 12.3 - Prob. 3CPCh. 12.3 - Prob. 4CPCh. 12.3 - Prob. 5CPCh. 12.3 - Checkpoint 6
In Example 9, suppose annual demand...Ch. 12.3 - Find the location of the absolute maximum and...Ch. 12.3 - Find the location of the absolute maximum and...Ch. 12.3 - Find the location of the absolute maximum and...Ch. 12.3 - Find the location of the absolute maximum and...Ch. 12.3 - Find the location of the absolute maximum and...Ch. 12.3 - Find the location of the absolute maximum and...Ch. 12.3 - Find the locations of the absolute extrema of each...Ch. 12.3 - Find the locations of the absolute extrema of each...Ch. 12.3 - Find the absolute extrema of each function on the...Ch. 12.3 - Find the absolute extrema of each function on the...Ch. 12.3 - Find the absolute extrema of each function on the...Ch. 12.3 - Find the absolute extrema of each function on the...Ch. 12.3 - Find the locations of the absolute extrema of each...Ch. 12.3 - Prob. 14ECh. 12.3 - Find the absolute extrema of each function on the...Ch. 12.3 - Find the absolute extrema of each function on the...Ch. 12.3 - Find the absolute extrema of each function on the...Ch. 12.3 - Prob. 18ECh. 12.3 - Prob. 19ECh. 12.3 - Prob. 20ECh. 12.3 - Prob. 21ECh. 12.3 - Prob. 23ECh. 12.3 - If possible, find an absolute extremum of each...Ch. 12.3 - If possible, find an absolute extremum of each...Ch. 12.3 - Prob. 26ECh. 12.3 - Work these problems. (See Example 5.)
25. Business...Ch. 12.3 - Work these problems. (See Example 5.)
26. Business...Ch. 12.3 - Work these exercises. Corporate Profits Total...Ch. 12.3 - Work these exercises.
30. Corporate Taxes For the...Ch. 12.3 - 31. Business A manufacturer produces gas grills...Ch. 12.3 - 32. Business Saltwater taffy can be sold wholesale...Ch. 12.3 - Work these exercises. Entertainment Expenditures...Ch. 12.3 - Work these exercises.
34. Consumer Spending...Ch. 12.3 - Work these exercises. Natural Science A lake...Ch. 12.3 - Prob. 38ECh. 12.3 - Prob. 39ECh. 12.3 - Prob. 40ECh. 12.3 - Prob. 41ECh. 12.3 - Prob. 42ECh. 12.3 - Prob. 43ECh. 12.3 - 42. Business A cylindrical can of volume 58 cubic...Ch. 12.3 - Prob. 45ECh. 12.3 - Prob. 46ECh. 12.3 - Prob. 47ECh. 12.3 - 46. Business A rectangular field is to be enclosed...Ch. 12.3 - 47. Business A mathematics book is to contain 36...Ch. 12.3 - Prob. 50ECh. 12.3 - 49. Business If the price charged for a candy bar...Ch. 12.3 - 50. Business A company makes plastic buckets for...Ch. 12.3 - 51. Business We can use the function
to model the...Ch. 12.3 - 52. Business A rock-and-roll band travels from...Ch. 12.3 - 53. Natural Science Homing pigeons avoid flying...Ch. 12.3 - 54. Business A company wishes to run a utility...Ch. 12.3 - Prob. 57ECh. 12.3 - Prob. 58ECh. 12.3 - Prob. 59ECh. 12.3 - Prob. 60ECh. 12.3 - Prob. 61ECh. 12.3 - 60. Business A restaurant has an annual demand for...Ch. 12.4 - Checkpoint 1
Find for
Ch. 12.4 - Prob. 2CPCh. 12.4 - Prob. 3CPCh. 12.4 - Prob. 4CPCh. 12.4 - Prob. 5CPCh. 12.4 - Prob. 6CPCh. 12.4 - Checkpoint 7
Suppose the sales function in Example...Ch. 12.4 - Prob. 1ECh. 12.4 - Prob. 2ECh. 12.4 - Find by implicit differentiation. (See Examples...Ch. 12.4 - Find by implicit differentiation. (See Examples...Ch. 12.4 - Prob. 5ECh. 12.4 - Prob. 6ECh. 12.4 - Prob. 7ECh. 12.4 - Prob. 8ECh. 12.4 - Prob. 9ECh. 12.4 - Prob. 10ECh. 12.4 - Prob. 11ECh. 12.4 - Find by implicit differentiation. (See Examples...Ch. 12.4 - Prob. 13ECh. 12.4 - Prob. 14ECh. 12.4 - Prob. 15ECh. 12.4 - Find by implicit differentiation. (See Examples...Ch. 12.4 - Prob. 17ECh. 12.4 - Prob. 18ECh. 12.4 - Prob. 19ECh. 12.4 - Find at the given point. (See Example 5.)
20.
Ch. 12.4 - Find at the given point. (See Example 5.)
21.
Ch. 12.4 - Prob. 22ECh. 12.4 - Prob. 23ECh. 12.4 - Find at the given point. (See Example 5.)
23.
Ch. 12.4 - Prob. 25ECh. 12.4 - Prob. 26ECh. 12.4 - Prob. 27ECh. 12.4 - Prob. 28ECh. 12.4 - Prob. 29ECh. 12.4 - Prob. 30ECh. 12.4 - Prob. 31ECh. 12.4 - Prob. 32ECh. 12.4 - Find the equation of the tangent line to the curve...Ch. 12.4 - Prob. 34ECh. 12.4 - Prob. 35ECh. 12.4 - Prob. 36ECh. 12.4 - Prob. 37ECh. 12.4 - Prob. 38ECh. 12.4 - Prob. 39ECh. 12.4 - Prob. 40ECh. 12.4 - 41. Business A night club has approximated the...Ch. 12.4 - 42. Business The demand to download a hit single...Ch. 12.4 - Work these exercises. Bank of America For Bank of...Ch. 12.4 - Work these exercises.
44. For the equation given...Ch. 12.4 - Work these exercises. Walt Disney Company The...Ch. 12.4 - Work these exercises.
46. For the equation given...Ch. 12.4 - Prob. 47ECh. 12.4 - 48. Business At a certain online printing service,...Ch. 12.5 - Checkpoint 1
Given that R3 = 25n4, find when n =...Ch. 12.5 - Prob. 2CPCh. 12.5 - Prob. 3CPCh. 12.5 - Prob. 4CPCh. 12.5 - Prob. 5CPCh. 12.5 - Prob. 6CPCh. 12.5 - Prob. 7CPCh. 12.5 - Given that x and y are functions of time, find the...Ch. 12.5 - Given that x and y are functions of time, find the...Ch. 12.5 - Given that x and y are functions of time, find the...Ch. 12.5 - Given that x and y are functions of time, find the...Ch. 12.5 - Prob. 5ECh. 12.5 - Prob. 6ECh. 12.5 - Prob. 7ECh. 12.5 - Prob. 8ECh. 12.5 - Prob. 9ECh. 12.5 - Given that x and y are functions of time, find the...Ch. 12.5 - Work these exercises. (See Examples 1, 3, and 4.)...Ch. 12.5 - Prob. 12ECh. 12.5 - Work these exercises. (See Examples 1, 3, and...Ch. 12.5 - Prob. 14ECh. 12.5 - Prob. 15ECh. 12.5 - Work these exercises. (See Examples 1, 3, and 4.)...Ch. 12.5 - Work these exercises. (See Examples 1, 3, and...Ch. 12.5 - Work these exercises. (See Examples 1, 3, and...Ch. 12.5 - Prob. 25ECh. 12.5 - Prob. 26ECh. 12.5 - Prob. 27ECh. 12.5 - Work these exercises. (See Examples 1, 3, and...Ch. 12.5 - 21. Business An architectural firm must decide on...Ch. 12.5 - 22. Social Science During a six-game hitless slump...Ch. 12.5 - Work these exercises. (See Example...Ch. 12.5 - Work these exercises. (See Example...Ch. 12.5 - Work these exercises.
27. Business The campus...Ch. 12.5 - Work these exercises.
28. Business Following a...Ch. 12.5 - 29. Business During a local political race, the...Ch. 12.5 - Prob. 20ECh. 12.5 - Work these exercises. Electricity from Coal and...Ch. 12.5 - Prob. 22ECh. 12.6 - Prob. 1CPCh. 12.6 - Prob. 2CPCh. 12.6 - Prob. 3CPCh. 12.6 - Prob. 4CPCh. 12.6 - Prob. 1ECh. 12.6 - Sketch the graph of the function. Identify any...Ch. 12.6 - Prob. 3ECh. 12.6 - Prob. 4ECh. 12.6 - Sketch the graph of the function. Identify any...Ch. 12.6 - Prob. 6ECh. 12.6 - Sketch the graph of the function. Identify any...Ch. 12.6 - Prob. 8ECh. 12.6 - Prob. 9ECh. 12.6 - Prob. 10ECh. 12.6 - Prob. 11ECh. 12.6 - Sketch the graph of the function. Identify any...Ch. 12.6 - Prob. 13ECh. 12.6 - Prob. 14ECh. 12.6 - Prob. 15ECh. 12.6 - Prob. 16ECh. 12.6 - Prob. 17ECh. 12.6 - Sketch the graph of the function. Identify any...Ch. 12.6 - Prob. 19ECh. 12.6 - Prob. 20ECh. 12.6 - Prob. 21ECh. 12.6 - Prob. 22ECh. 12.6 - Prob. 23ECh. 12.6 - In Exercises 23–28, sketch the graph of a function...Ch. 12.6 - Prob. 25ECh. 12.6 - In Exercises 23–28, sketch the graph of a function...Ch. 12.6 - In Exercises 23–28, sketch the graph of a function...Ch. 12.6 - In Exercises 23–28, sketch the graph of a function...Ch. 12.6 - 29. Business The accompanying figure shows the...Ch. 12.6 - 30. Refer to the graph in Exercise 29. Which...Ch. 12.6 - Prob. 31ECh. 12.6 - Work these exercises. Average Temperature During...Ch. 12.6 - Prob. 33ECh. 12.6 - Prob. 34ECh. 12.6 - Prob. 35ECh. 12.6 - Prob. 36ECh. 12 - Prob. 1RECh. 12 - Prob. 2RECh. 12 - Prob. 3RECh. 12 - Prob. 4RECh. 12 - Prob. 5RECh. 12 - Prob. 6RECh. 12 - Prob. 7RECh. 12 - Prob. 8RECh. 12 - Prob. 9RECh. 12 - Prob. 10RECh. 12 - Prob. 11RECh. 12 - Prob. 12RECh. 12 - Prob. 13RECh. 12 - Prob. 14RECh. 12 - Prob. 15RECh. 12 - Prob. 16RECh. 12 - Prob. 17RECh. 12 - Prob. 18RECh. 12 - Prob. 19RECh. 12 - Prob. 20RECh. 12 - Prob. 21RECh. 12 - Prob. 22RECh. 12 - Prob. 23RECh. 12 - Prob. 24RECh. 12 - Prob. 25RECh. 12 - Prob. 26RECh. 12 - Prob. 27RECh. 12 - Prob. 28RECh. 12 - Prob. 29RECh. 12 - Prob. 30RECh. 12 - Prob. 31RECh. 12 - Prob. 32RECh. 12 - Prob. 33RECh. 12 - Prob. 34RECh. 12 - Prob. 35RECh. 12 - Prob. 36RECh. 12 - Prob. 37RECh. 12 - Prob. 38RECh. 12 - Prob. 39RECh. 12 - Prob. 40RECh. 12 - Prob. 41RECh. 12 - Prob. 42RECh. 12 - Prob. 43RECh. 12 - Prob. 44RECh. 12 - Prob. 45RECh. 12 - Prob. 46RECh. 12 - Prob. 47RECh. 12 - Prob. 48RECh. 12 - Prob. 49RECh. 12 - Work these exercises. Olympic High Jump The gold...Ch. 12 - Prob. 51RECh. 12 - Prob. 52RECh. 12 - Prob. 53RECh. 12 - Prob. 54RECh. 12 - Prob. 55RECh. 12 - Prob. 56RECh. 12 - Prob. 57RECh. 12 - Prob. 58RECh. 12 - 59. Business A landscaper needs to design an...Ch. 12 - Prob. 60RECh. 12 - Prob. 61RECh. 12 - Prob. 62RECh. 12 - Prob. 63RECh. 12 - 64. Business How many phones need to be produced...Ch. 12 - Prob. 65RECh. 12 - Prob. 66RECh. 12 - Prob. 67RECh. 12 - Prob. 68RECh. 12 - Prob. 69RECh. 12 - Prob. 70RECh. 12 - Prob. 71RECh. 12 - Prob. 72RECh. 12 - Prob. 73RECh. 12 - 74. Social Science A baseball player hits the ball...Ch. 12 - Prob. 1CECh. 12 - Prob. 2CECh. 12 - Prob. 3CECh. 12 - Prob. 4CECh. 12 - Prob. 5CECh. 12 - 6. What is the optimum time interval between...Ch. 12 - A pharmaceutical company is planning to gradually...
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- (7) (12 points) Let F(x, y, z) = (y, x+z cos yz, y cos yz). Ꮖ (a) (4 points) Show that V x F = 0. (b) (4 points) Find a potential f for the vector field F. (c) (4 points) Let S be a surface in R3 for which the Stokes' Theorem is valid. Use Stokes' Theorem to calculate the line integral Jos F.ds; as denotes the boundary of S. Explain your answer.arrow_forward(3) (16 points) Consider z = uv, u = x+y, v=x-y. (a) (4 points) Express z in the form z = fog where g: R² R² and f: R² → R. (b) (4 points) Use the chain rule to calculate Vz = (2, 2). Show all intermediate steps otherwise no credit. (c) (4 points) Let S be the surface parametrized by T(x, y) = (x, y, ƒ (g(x, y)) (x, y) = R². Give a parametric description of the tangent plane to S at the point p = T(x, y). (d) (4 points) Calculate the second Taylor polynomial Q(x, y) (i.e. the quadratic approximation) of F = (fog) at a point (a, b). Verify that Q(x,y) F(a+x,b+y). =arrow_forward(6) (8 points) Change the order of integration and evaluate (z +4ry)drdy . So S√ ² 0arrow_forward
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