Precalculus (MindTap Course List)
10th Edition
ISBN: 9781337271073
Author: Ron Larson
Publisher: Cengage Learning
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Chapter A.7, Problem 1CP
To determine
To describe:
And correct the error of the given function
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(3) (20 points) Let F(x, y, z) = (y, z, x²z). Define
E = {(x, y, z) | x² + y² ≤ z ≤ 1, x ≤ 0}.
(a) (2 points) Calculate the divergence V. F.
(b) (4 points) Let D = {(x, y) | x² + y² ≤ 1, x ≤ 0} Without calculation, show that
the triple integral
√ (V · F) dV = √ 2²(1.
= x²(1 − x² - y²) dA.
E
(2) (22 points) Let F(x, y, z) = (x sin y, cos y, ―xy).
(a) (2 points) Calculate V. F.
(b) (6 points) Given a vector field
is everywhere defined with V
G₁(x, y, z) = *
G2(x, y, z) = −
G3(x, y, z) = 0.
0
0
F(x, y, z) = (F₁(x, y, z), F₂(x, y, z), F(x, y, z)) that
F = 0, let G = (G1, G2, G3) where
F₂(x,
y,
y, t) dt
- √ F³(x, t, 0) dt,
*
F1(x,
y, t) dt,
t) dt - √ F
Calculate G for the vector field F(x, y, z) = (x sin y, cos y, -xy).
Evaluate the following integral over the Region R.
(Answer accurate to 2 decimal places).
√ √(x + y) A
R
R = {(x, y) | 25 < x² + y² ≤ 36, x < 0}
Hint: The integral and Region is defined in rectangular coordinates.
Chapter A Solutions
Precalculus (MindTap Course List)
Ch. A.1 - Checkpoint Repeat Example 1 for the set...Ch. A.1 - Checkpoint Plot the real numbers on the real...Ch. A.1 - Prob. 3CPCh. A.1 - Prob. 4CPCh. A.1 - Prob. 5CPCh. A.1 - Prob. 6CPCh. A.1 - Prob. 7CPCh. A.1 - Prob. 8CPCh. A.1 - Prob. 9CPCh. A.1 - Prob. 10CP
Ch. A.1 - Prob. 11CPCh. A.1 - Prob. 12CPCh. A.1 - Prob. 13CPCh. A.1 - Prob. 14CPCh. A.1 - Vocabulary: Fill in the blanks. The decimal...Ch. A.1 - Prob. 2ECh. A.1 - Prob. 3ECh. A.1 - Prob. 4ECh. A.1 - Prob. 5ECh. A.1 - Prob. 6ECh. A.1 - Prob. 7ECh. A.1 - Prob. 8ECh. A.1 - Prob. 9ECh. A.1 - Prob. 10ECh. A.1 - Prob. 11ECh. A.1 - Prob. 12ECh. A.1 - Prob. 13ECh. A.1 - Prob. 14ECh. A.1 - Prob. 15ECh. A.1 - Prob. 16ECh. A.1 - Skills and Applications Interpreting an Inequality...Ch. A.1 - Skills and Applications Interpreting an Inequality...Ch. A.1 - Prob. 19ECh. A.1 - Prob. 20ECh. A.1 - Prob. 21ECh. A.1 - Prob. 22ECh. A.1 - Prob. 23ECh. A.1 - Prob. 24ECh. A.1 - Skills and Applications Using Inequality or an...Ch. A.1 - Skills and Applications Using Inequality or an...Ch. A.1 - Prob. 27ECh. A.1 - Prob. 28ECh. A.1 - Prob. 29ECh. A.1 - Prob. 30ECh. A.1 - Prob. 31ECh. A.1 - Prob. 32ECh. A.1 - Prob. 33ECh. A.1 - Prob. 34ECh. A.1 - Prob. 35ECh. A.1 - Prob. 36ECh. A.1 - Prob. 37ECh. A.1 - Prob. 38ECh. A.1 - Prob. 39ECh. A.1 - Prob. 40ECh. A.1 - Prob. 41ECh. A.1 - Prob. 42ECh. A.1 - Prob. 43ECh. A.1 - Prob. 44ECh. A.1 - Prob. 45ECh. A.1 - Prob. 46ECh. A.1 - Skills and Applications Using Absolute Value...Ch. A.1 - Skills and Applications Using Absolute Value...Ch. A.1 - Prob. 49ECh. A.1 - Prob. 50ECh. A.1 - Prob. 51ECh. A.1 - Prob. 52ECh. A.1 - Prob. 53ECh. A.1 - Prob. 54ECh. A.1 - Prob. 55ECh. A.1 - Prob. 56ECh. A.1 - Prob. 57ECh. A.1 - Prob. 58ECh. A.1 - Prob. 59ECh. A.1 - Prob. 60ECh. A.1 - Prob. 61ECh. A.1 - Prob. 62ECh. A.1 - Prob. 63ECh. A.1 - Prob. 64ECh. A.1 - Prob. 65ECh. A.1 - Prob. 66ECh. A.1 - Prob. 67ECh. A.1 - Prob. 68ECh. A.1 - Prob. 69ECh. A.1 - Prob. 70ECh. A.1 - Prob. 71ECh. A.1 - Prob. 72ECh. A.1 - Prob. 73ECh. A.1 - Prob. 74ECh. A.1 - Prob. 75ECh. A.1 - Exploration HOW DO YOU SEE IT? Match each...Ch. A.1 - Prob. 77ECh. A.2 - Checkpoint Evaluate each expression a. 34 b. (3)4...Ch. A.2 - Prob. 2CPCh. A.2 - Prob. 3CPCh. A.2 - Prob. 4CPCh. A.2 - Prob. 5CPCh. A.2 - Prob. 6CPCh. A.2 - Prob. 7CPCh. A.2 - Prob. 8CPCh. A.2 - Prob. 9CPCh. A.2 - Simplify each radical expression. a. 32 b. 2503 c....Ch. A.2 - Prob. 11CPCh. A.2 - Prob. 12CPCh. A.2 - Prob. 13CPCh. A.2 - Prob. 14CPCh. A.2 - Prob. 15CPCh. A.2 - Prob. 16CPCh. A.2 - Prob. 17CPCh. A.2 - Prob. 1ECh. A.2 - Prob. 2ECh. A.2 - Prob. 3ECh. A.2 - Prob. 4ECh. A.2 - Prob. 5ECh. A.2 - Fill in the blanks The expressions a+bm and abm...Ch. A.2 - Prob. 7ECh. A.2 - Prob. 8ECh. A.2 - Prob. 9ECh. A.2 - Skills and Applications Evaluating Exponential...Ch. A.2 - Prob. 11ECh. A.2 - Prob. 12ECh. A.2 - Prob. 13ECh. A.2 - Prob. 14ECh. A.2 - Prob. 15ECh. A.2 - Prob. 16ECh. A.2 - Prob. 17ECh. A.2 - Prob. 18ECh. A.2 - Prob. 19ECh. A.2 - Prob. 20ECh. A.2 - Prob. 21ECh. A.2 - Prob. 22ECh. A.2 - Prob. 23ECh. A.2 - Prob. 24ECh. A.2 - Prob. 25ECh. A.2 - Prob. 26ECh. A.2 - Prob. 27ECh. A.2 - Prob. 28ECh. A.2 - Prob. 29ECh. A.2 - Prob. 30ECh. A.2 - Prob. 31ECh. A.2 - Prob. 32ECh. A.2 - Prob. 33ECh. A.2 - Decimal Notation In Exercises 33-36, write the...Ch. A.2 - Prob. 35ECh. A.2 - Prob. 36ECh. A.2 - Prob. 37ECh. A.2 - Prob. 38ECh. A.2 - Prob. 39ECh. A.2 - Prob. 40ECh. A.2 - Prob. 41ECh. A.2 - Prob. 42ECh. A.2 - Prob. 43ECh. A.2 - Prob. 44ECh. A.2 - Prob. 45ECh. A.2 - Prob. 46ECh. A.2 - Prob. 47ECh. A.2 - Prob. 48ECh. A.2 - Prob. 49ECh. A.2 - Prob. 50ECh. A.2 - Prob. 51ECh. A.2 - Prob. 52ECh. A.2 - Prob. 53ECh. A.2 - Prob. 54ECh. A.2 - Prob. 55ECh. A.2 - Prob. 56ECh. A.2 - Prob. 57ECh. A.2 - Prob. 58ECh. A.2 - Prob. 59ECh. A.2 - Prob. 60ECh. A.2 - Prob. 61ECh. A.2 - Prob. 62ECh. A.2 - Prob. 63ECh. A.2 - Prob. 64ECh. A.2 - Prob. 65ECh. A.2 - Prob. 66ECh. A.2 - Prob. 67ECh. A.2 - Prob. 68ECh. A.2 - Prob. 69ECh. A.2 - Prob. 70ECh. A.2 - Prob. 71ECh. A.2 - Prob. 72ECh. A.2 - Prob. 73ECh. A.2 - Prob. 74ECh. A.3 - Prob. 1CPCh. A.3 - Prob. 2CPCh. A.3 - Prob. 3CPCh. A.3 - Prob. 4CPCh. A.3 - Prob. 5CPCh. A.3 - Prob. 6CPCh. A.3 - Prob. 7CPCh. A.3 - Prob. 8CPCh. A.3 - Prob. 9CPCh. 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A.3 - Prob. 48ECh. A.3 - Prob. 49ECh. A.3 - Prob. 50ECh. A.3 - Prob. 51ECh. A.3 - Prob. 52ECh. A.3 - Prob. 53ECh. A.3 - Prob. 54ECh. A.3 - Prob. 55ECh. A.3 - Prob. 56ECh. A.3 - Prob. 57ECh. A.3 - Prob. 58ECh. A.3 - Prob. 59ECh. A.3 - Prob. 60ECh. A.3 - Prob. 61ECh. A.3 - Prob. 62ECh. A.3 - Prob. 63ECh. A.3 - Prob. 64ECh. A.3 - Prob. 65ECh. A.3 - Prob. 66ECh. A.3 - Prob. 67ECh. A.3 - Prob. 68ECh. A.3 - Prob. 69ECh. A.3 - Prob. 70ECh. A.3 - Prob. 71ECh. A.3 - Prob. 72ECh. A.3 - Prob. 73ECh. A.3 - Prob. 74ECh. A.3 - Prob. 75ECh. A.3 - Prob. 76ECh. A.3 - Prob. 77ECh. A.3 - Prob. 78ECh. A.3 - Factoring Completely In Exercises 73-82,...Ch. A.3 - Prob. 80ECh. A.3 - Prob. 81ECh. A.3 - Prob. 82ECh. A.3 - Prob. 83ECh. A.3 - Prob. 84ECh. A.3 - Prob. 85ECh. A.3 - Prob. 86ECh. A.3 - True or False In Exercises 85-87, determine...Ch. A.3 - Prob. 88ECh. A.3 - Prob. 89ECh. A.3 - Prob. 90ECh. A.3 - Prob. 91ECh. A.3 - Prob. 92ECh. A.3 - Prob. 93ECh. A.3 - Prob. 94ECh. A.3 - Prob. 95ECh. A.3 - Prob. 96ECh. A.4 - Prob. 1CPCh. A.4 - Prob. 2CPCh. A.4 - Prob. 3CPCh. A.4 - Prob. 4CPCh. A.4 - Prob. 5CPCh. A.4 - Prob. 6CPCh. A.4 - Prob. 7CPCh. A.4 - Prob. 8CPCh. A.4 - Prob. 9CPCh. A.4 - Prob. 10CPCh. A.4 - Prob. 11CPCh. A.4 - A.4 Exercises Vocabulary: Fill in the blanks. The...Ch. A.4 - A.4 Exercises Vocabulary: Fill in the blanks. The...Ch. A.4 - Prob. 3ECh. A.4 - Prob. 4ECh. A.4 - Prob. 5ECh. A.4 - Prob. 6ECh. A.4 - Prob. 7ECh. A.4 - Prob. 8ECh. A.4 - Prob. 9ECh. A.4 - Prob. 10ECh. A.4 - Prob. 11ECh. A.4 - Prob. 12ECh. A.4 - Prob. 13ECh. A.4 - Prob. 14ECh. A.4 - Prob. 15ECh. A.4 - Prob. 16ECh. A.4 - Prob. 17ECh. A.4 - Prob. 18ECh. A.4 - Prob. 19ECh. A.4 - Prob. 20ECh. A.4 - Prob. 21ECh. A.4 - Prob. 22ECh. A.4 - Prob. 23ECh. A.4 - Prob. 24ECh. A.4 - Prob. 25ECh. A.4 - Prob. 26ECh. A.4 - Prob. 27ECh. A.4 - Prob. 28ECh. A.4 - Prob. 29ECh. A.4 - Prob. 30ECh. A.4 - Prob. 31ECh. A.4 - Prob. 32ECh. A.4 - Prob. 33ECh. A.4 - Prob. 34ECh. A.4 - Prob. 35ECh. A.4 - Prob. 36ECh. A.4 - Prob. 37ECh. A.4 - Prob. 38ECh. A.4 - Prob. 39ECh. A.4 - Prob. 40ECh. A.4 - Prob. 41ECh. A.4 - Prob. 42ECh. A.4 - Prob. 43ECh. A.4 - Prob. 44ECh. A.4 - Prob. 45ECh. A.4 - Prob. 46ECh. A.4 - Prob. 47ECh. A.4 - Prob. 48ECh. A.4 - Prob. 49ECh. A.4 - Prob. 50ECh. A.4 - Prob. 51ECh. A.4 - Prob. 52ECh. A.4 - Prob. 53ECh. A.4 - Prob. 54ECh. A.4 - Prob. 55ECh. A.4 - Prob. 56ECh. A.4 - Prob. 57ECh. A.4 - Prob. 58ECh. A.4 - Prob. 59ECh. A.4 - Prob. 60ECh. A.4 - Prob. 61ECh. A.4 - Prob. 62ECh. A.4 - Prob. 63ECh. A.4 - Prob. 64ECh. A.4 - Prob. 65ECh. A.4 - Prob. 66ECh. A.4 - Prob. 67ECh. A.4 - Prob. 68ECh. A.4 - Rewriting a Difference Quotient In Exercises 6570,...Ch. A.4 - Prob. 70ECh. A.4 - Prob. 71ECh. A.4 - Prob. 72ECh. A.4 - Prob. 73ECh. A.4 - Prob. 74ECh. A.4 - Prob. 75ECh. A.4 - Prob. 76ECh. A.4 - Prob. 77ECh. A.4 - Prob. 78ECh. A.4 - Prob. 79ECh. A.4 - Prob. 80ECh. A.5 - Prob. 1CPCh. A.5 - Prob. 2CPCh. A.5 - Prob. 3CPCh. A.5 - Prob. 4CPCh. A.5 - Prob. 5CPCh. A.5 - Prob. 6CPCh. A.5 - Prob. 7CPCh. A.5 - Prob. 8CPCh. A.5 - Prob. 9CPCh. A.5 - Prob. 10CPCh. A.5 - Prob. 11CPCh. A.5 - Checkpoint Solve -40-9x+2=x.Ch. A.5 - Prob. 13CPCh. A.5 - Checkpoint Solve x2+4x=7x+18 and check your...Ch. A.5 - Prob. 15CPCh. A.5 - Prob. 1ECh. A.5 - Prob. 2ECh. A.5 - Prob. 3ECh. A.5 - Prob. 4ECh. A.5 - Prob. 5ECh. A.5 - Prob. 6ECh. A.5 - Prob. 7ECh. A.5 - Prob. 8ECh. A.5 - Prob. 9ECh. A.5 - Prob. 10ECh. A.5 - Prob. 11ECh. A.5 - Prob. 12ECh. A.5 - Prob. 13ECh. A.5 - Skills and Applications Solving a Rational...Ch. A.5 - Prob. 15ECh. A.5 - Prob. 16ECh. A.5 - Prob. 17ECh. A.5 - Skills and Applications Solving a Rational...Ch. A.5 - Prob. 19ECh. A.5 - Prob. 20ECh. A.5 - Prob. 21ECh. A.5 - Prob. 22ECh. A.5 - Prob. 23ECh. A.5 - Prob. 24ECh. A.5 - Prob. 25ECh. A.5 - Prob. 26ECh. A.5 - Prob. 27ECh. A.5 - Prob. 28ECh. A.5 - Prob. 29ECh. A.5 - Prob. 30ECh. A.5 - Prob. 31ECh. A.5 - Prob. 32ECh. A.5 - Prob. 33ECh. A.5 - Prob. 34ECh. A.5 - Prob. 35ECh. A.5 - Prob. 36ECh. A.5 - Prob. 37ECh. 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A.5 - Prob. 88ECh. A.5 - Prob. 89ECh. A.5 - Prob. 90ECh. A.5 - Prob. 91ECh. A.5 - Prob. 92ECh. A.5 - Skills and Applications: Volume of a Billiard Ball...Ch. A.5 - Prob. 94ECh. A.5 - Skills and Applications: Forensics In Exercises 95...Ch. A.5 - Skills and Applications: Forensics In Exercises 95...Ch. A.5 - Prob. 97ECh. A.5 - Prob. 98ECh. A.5 - Prob. 99ECh. A.5 - Prob. 100ECh. A.6 - Write an inequality that represents each interval....Ch. A.6 - Prob. 2CPCh. A.6 - Prob. 3CPCh. A.6 - Prob. 4CPCh. A.6 - Prob. 5CPCh. A.6 - Prob. 6CPCh. A.6 - Prob. 7CPCh. A.6 - Prob. 1ECh. A.6 - Prob. 2ECh. A.6 - Fill in the blanks It is sometimes possible to...Ch. A.6 - Prob. 4ECh. A.6 - Prob. 5ECh. A.6 - Prob. 6ECh. A.6 - Prob. 7ECh. A.6 - Prob. 8ECh. A.6 - Prob. 9ECh. A.6 - Prob. 10ECh. A.6 - Intervals and Inequalities In Exercises 5-12,...Ch. A.6 - Prob. 12ECh. A.6 - Solving a Linear Inequality In Exercises 13-30,...Ch. A.6 - Prob. 14ECh. A.6 - Prob. 15ECh. A.6 - Prob. 16ECh. A.6 - Prob. 17ECh. A.6 - Prob. 18ECh. A.6 - Prob. 19ECh. A.6 - Prob. 20ECh. A.6 - Prob. 21ECh. A.6 - Prob. 22ECh. A.6 - Prob. 23ECh. A.6 - Prob. 24ECh. A.6 - Prob. 25ECh. A.6 - Prob. 26ECh. A.6 - Prob. 27ECh. A.6 - Prob. 28ECh. A.6 - Prob. 29ECh. A.6 - Prob. 30ECh. A.6 - Prob. 31ECh. A.6 - Prob. 32ECh. A.6 - Prob. 33ECh. A.6 - Prob. 34ECh. A.6 - Prob. 35ECh. A.6 - Prob. 36ECh. A.6 - Solving a Double Inequality In Exercises 31-42,...Ch. A.6 - Prob. 38ECh. A.6 - Prob. 39ECh. A.6 - Prob. 40ECh. A.6 - Prob. 41ECh. A.6 - Prob. 42ECh. A.6 - Prob. 43ECh. A.6 - Prob. 44ECh. A.6 - Prob. 45ECh. A.6 - Prob. 46ECh. A.6 - Prob. 47ECh. A.6 - Prob. 48ECh. A.6 - Prob. 49ECh. A.6 - Prob. 50ECh. A.6 - Prob. 51ECh. A.6 - Prob. 52ECh. A.6 - Prob. 53ECh. A.6 - Prob. 54ECh. A.6 - Prob. 55ECh. A.6 - Prob. 56ECh. A.6 - Prob. 57ECh. A.6 - Prob. 58ECh. A.6 - Prob. 59ECh. A.6 - Prob. 60ECh. A.6 - Prob. 61ECh. A.6 - Prob. 62ECh. A.6 - Prob. 63ECh. A.6 - Prob. 64ECh. A.6 - Prob. 65ECh. A.6 - Prob. 66ECh. A.6 - Prob. 67ECh. A.6 - Prob. 68ECh. A.6 - Prob. 69ECh. A.6 - Prob. 70ECh. A.6 - Prob. 71ECh. A.6 - Prob. 72ECh. A.6 - Prob. 73ECh. A.6 - Prob. 74ECh. A.6 - Prob. 75ECh. A.6 - Prob. 76ECh. A.6 - Using Absolute Value In Exercises 77-84, use...Ch. A.6 - Prob. 78ECh. A.6 - Prob. 79ECh. A.6 - Prob. 80ECh. A.6 - Using Absolute Value In Exercises 77-84, use...Ch. A.6 - Prob. 82ECh. A.6 - Prob. 83ECh. A.6 - Using Absolute Value In Exercises 77-84, use...Ch. A.6 - Prob. 85ECh. A.6 - Prob. 86ECh. A.6 - Prob. 87ECh. A.6 - Prob. 88ECh. A.6 - Prob. 89ECh. A.6 - Prob. 90ECh. A.6 - Job Offers You are considering two job offers. The...Ch. A.6 - Job Offers You are considering two job offers. The...Ch. A.6 - Prob. 93ECh. A.6 - Prob. 94ECh. A.6 - Prob. 95ECh. A.6 - Cost, Revenue, and Profit The revenue from selling...Ch. A.6 - Prob. 97ECh. A.6 - Prob. 98ECh. A.6 - GPA An equation that relates the college...Ch. A.6 - Prob. 100ECh. A.6 - Prob. 101ECh. A.6 - Milk Production Milk production M in billions of...Ch. 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- Find the volume of the solid that lies under the paraboloid z = 81 - x² - y² and within the cylinder (x − 1)² + y² = 1. A plot of an example of a similar solid is shown below. (Answer accurate to 2 decimal places). Volume using Double Integral Paraboloid & Cylinder -3 Hint: The integral and region is defined in polar coordinates.arrow_forwardEvaluate the following integral over the Region R. (Answer accurate to 2 decimal places). √4(1–2² 4(1 - x² - y²) dA R 3 R = {(r,0) | 0 ≤ r≤ 2,0π ≤0≤¼˜}. Hint: The integral is defined in rectangular coordinates. The Region is defined in polar coordinates.arrow_forwardEvaluate the following integral over the Region R. (Answer accurate to 2 decimal places). R - 1 · {(r,0) | 1 ≤ r≤ 5,½π≤ 0<1π}. Hint: Be sure to convert to Polar coordinates. Use the correct differential for Polar Coordinates.arrow_forward
- Evaluate the following integral over the Region R. (Answer accurate to 2 decimal places). √ √2(x+y) dA R R = {(x, y) | 4 < x² + y² < 25,0 < x} Hint: The integral and Region is defined in rectangular coordinates.arrow_forwardHW: The frame shown in the figure is pinned at A and C. Use moment distribution method, with and without modifications, to draw NFD, SFD, and BMD. B I I 40 kN/m A 3 m 4 marrow_forwardLet the region R be the area enclosed by the function f(x)= = 3x² and g(x) = 4x. If the region R is the base of a solid such that each cross section perpendicular to the x-axis is an isosceles right triangle with a leg in the region R, find the volume of the solid. You may use a calculator and round to the nearest thousandth. y 11 10 9 00 8 7 9 5 4 3 2 1 -1 -1 x 1 2arrow_forward
- Let the region R be the area enclosed by the function f(x) = ex — 1, the horizontal line y = -4 and the vertical lines x = 0 and x = 3. Find the volume of the solid generated when the region R is revolved about the line y = -4. You may use a calculator and round to the nearest thousandth. 20 15 10 5 y I I I | I + -1.5 -1 -0.5 0.5 1 1.5 2 2.5 3 -5 I -10 -15 I + I I T I I + -20 I + -25 I I I -30 I 3.5 4 xarrow_forwardplease show all the workarrow_forwardplease show all the workarrow_forward
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