EBK THOMAS'CALCULUS,EARLY TRANSCEND.
14th Edition
ISBN: 9780134606095
Author: Hass
Publisher: PEARSON
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Chapter 14.3, Problem 5E
To determine
Calculate the first order partial derivatives
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Chapter 14 Solutions
EBK THOMAS'CALCULUS,EARLY TRANSCEND.
Ch. 14.1 - In Exercises 1–4, find the specific function...Ch. 14.1 - In Exercises 1–4, find the specific function...Ch. 14.1 - In Exercises 1–4, find the specific function...Ch. 14.1 - In Exercises 1–4, find the specific function...Ch. 14.1 - In Exercises 5–12, find and sketch the domain for...Ch. 14.1 - In Exercises 5–12, find and sketch the domain for...Ch. 14.1 - In Exercises 5–12, find and sketch the domain for...Ch. 14.1 - In Exercises 5–12, find and sketch the domain for...Ch. 14.1 - In Exercises 5–12, find and sketch the domain for...Ch. 14.1 - In Exercises 5–12, find and sketch the domain for...
Ch. 14.1 - In Exercises 5–12, find and sketch the domain for...Ch. 14.1 - In Exercises 5–12, find and sketch the domain for...Ch. 14.1 - In Exercises 13–16, find and sketch the level...Ch. 14.1 - In Exercises 13–16, find and sketch the level...Ch. 14.1 - In Exercises 13–16, find and sketch the level...Ch. 14.1 - In Exercises 13–16, find and sketch the level...Ch. 14.1 - In Exercises 17-30, (a) find the function’s...Ch. 14.1 - In Exercises 17-30, (a) find the function’s...Ch. 14.1 - In Exercises 17-30, (a) find the function’s...Ch. 14.1 - In Exercises 17-30, (a) find the function’s...Ch. 14.1 - In Exercises 17-30, (a) find the function’s...Ch. 14.1 - In Exercises 17-30, (a) find the function’s...Ch. 14.1 - In Exercises 17-30, (a) find the function’s...Ch. 14.1 - In Exercises 17-30, (a) find the function’s...Ch. 14.1 - In Exercises 17-30, (a) find the function’s...Ch. 14.1 - In Exercises 17-30, (a) find the function’s...Ch. 14.1 - In Exercises 17-30, (a) find the function’s...Ch. 14.1 - In Exercises 17-30, (a) find the function’s...Ch. 14.1 - In Exercises 17–30, (a) find the function’s...Ch. 14.1 - In Exercises 17–30, (a) find the function’s...Ch. 14.1 - Exercises 31–36 show level curves for six...Ch. 14.1 - Prob. 32ECh. 14.1 - Prob. 33ECh. 14.1 - Exercises 31–36 show level curves for six...Ch. 14.1 - Prob. 35ECh. 14.1 - Prob. 36ECh. 14.1 - Display the values of the functions in Exercises...Ch. 14.1 - Prob. 38ECh. 14.1 - Prob. 39ECh. 14.1 - Display the values of the functions in Exercises...Ch. 14.1 - Prob. 41ECh. 14.1 - Prob. 42ECh. 14.1 - Prob. 43ECh. 14.1 - Prob. 44ECh. 14.1 - Prob. 45ECh. 14.1 - Display the values of the functions in Exercises...Ch. 14.1 - Prob. 47ECh. 14.1 - Prob. 48ECh. 14.1 - In Exercises 49–52, find an equation for, and...Ch. 14.1 - In Exercises 49–52, find an equation for, and...Ch. 14.1 - In Exercises 49–52, find an equation for, and...Ch. 14.1 - In Exercises 49–52, find an equation for, and...Ch. 14.1 - In Exercises 53–60, sketch a typical level surface...Ch. 14.1 - In Exercises 53–60, sketch a typical level surface...Ch. 14.1 - In Exercises 53–60, sketch a typical level surface...Ch. 14.1 - In Exercises 53–60, sketch a typical level surface...Ch. 14.1 - Prob. 57ECh. 14.1 - Prob. 58ECh. 14.1 - Prob. 59ECh. 14.1 - Prob. 60ECh. 14.1 - In Exercises 61–64, find an equation for the level...Ch. 14.1 - In Exercises 61–64, find an equation for the level...Ch. 14.1 - In Exercises 61–64, find an equation for the level...Ch. 14.1 - In Exercises 61–64, find an equation for the level...Ch. 14.1 - In Exercises 65–68, find and sketch the domain of...Ch. 14.1 - In Exercises 65–68, find and sketch the domain of...Ch. 14.1 - In Exercises 65–68, find and sketch the domain of...Ch. 14.1 - In Exercises 65–68, find and sketch the domain of...Ch. 14.2 - Find the limits in Exercises 1–12.
1.
Ch. 14.2 - Find the limits in Exercises 1–12.
2.
Ch. 14.2 - Find the limits in Exercises 1–12.
3.
Ch. 14.2 - Find the limits in Exercises 1–12.
4.
Ch. 14.2 - Find the limits in Exercises 1–12.
5.
Ch. 14.2 - Find the limits in Exercises 1–12.
6.
Ch. 14.2 - Find the limits in Exercises 1–12.
7.
Ch. 14.2 - Find the limits in Exercises 1–12.
8.
Ch. 14.2 - Find the limits in Exercises 1–12.
9.
Ch. 14.2 - Find the limits in Exercises 1–12.
10.
Ch. 14.2 - Find the limits in Exercises 1–12.
11.
Ch. 14.2 - Find the limits in Exercises 1–12.
12.
Ch. 14.2 - Find the limits in Exercises 13–24 by rewriting...Ch. 14.2 - Find the limits in Exercises 13–24 by rewriting...Ch. 14.2 - Find the limits in Exercises 13–24 by rewriting...Ch. 14.2 - Find the limits in Exercises 13–24 by rewriting...Ch. 14.2 - Find the limits in Exercises 13–24 by rewriting...Ch. 14.2 - Find the limits in Exercises 13–24 by rewriting...Ch. 14.2 - Find the limits in Exercises 13–24 by rewriting...Ch. 14.2 - Find the limits in Exercises 13–24 by rewriting...Ch. 14.2 - Find the limits in Exercises 13–24 by rewriting...Ch. 14.2 - Find the limits in Exercises 13–24 by rewriting...Ch. 14.2 - Find the limits in Exercises 13–24 by rewriting...Ch. 14.2 - Find the limits in Exercises 13–24 by rewriting...Ch. 14.2 - Find the limits in Exercises 25–30.
25.
Ch. 14.2 - Find the limits in Exercises 25–30.
26.
Ch. 14.2 - Find the limits in Exercises 25–30.
27.
Ch. 14.2 - Find the limits in Exercises 25–30.
28.
Ch. 14.2 - Find the limits in Exercises 25–30.
29.
Ch. 14.2 - Find the limits in Exercises 25–30.
30.
Ch. 14.2 - Prob. 31ECh. 14.2 - Prob. 32ECh. 14.2 - Prob. 33ECh. 14.2 - Prob. 34ECh. 14.2 - Prob. 35ECh. 14.2 - Prob. 36ECh. 14.2 - Prob. 37ECh. 14.2 - Prob. 38ECh. 14.2 - At what points (x, y, z) in space are the...Ch. 14.2 - Prob. 40ECh. 14.2 - By considering different paths of approach, show...Ch. 14.2 - Prob. 42ECh. 14.2 - By considering different paths of approach, show...Ch. 14.2 - Prob. 44ECh. 14.2 - Prob. 45ECh. 14.2 - By considering different paths of approach, show...Ch. 14.2 - By considering different paths of approach, show...Ch. 14.2 - Prob. 48ECh. 14.2 - In Exercises 49–54, show that the limits do not...Ch. 14.2 - Prob. 50ECh. 14.2 - Prob. 51ECh. 14.2 - In Exercises 49–54, show that the limits do not...Ch. 14.2 - Prob. 53ECh. 14.2 - Prob. 54ECh. 14.2 - Prob. 55ECh. 14.2 - Prob. 56ECh. 14.2 - Prob. 57ECh. 14.2 - Prob. 58ECh. 14.2 - Prob. 59ECh. 14.2 - Prob. 60ECh. 14.2 - Prob. 61ECh. 14.2 - Prob. 62ECh. 14.2 - Prob. 63ECh. 14.2 - Prob. 64ECh. 14.2 - Prob. 65ECh. 14.2 - Prob. 66ECh. 14.2 - Prob. 67ECh. 14.2 - Prob. 68ECh. 14.2 - Prob. 69ECh. 14.2 - Prob. 70ECh. 14.2 - Prob. 71ECh. 14.2 - Prob. 72ECh. 14.2 - Prob. 73ECh. 14.2 - Prob. 74ECh. 14.2 - Prob. 75ECh. 14.2 - Prob. 76ECh. 14.2 - Prob. 77ECh. 14.2 - Prob. 78ECh. 14.2 - Prob. 79ECh. 14.2 - Prob. 80ECh. 14.2 - Prob. 81ECh. 14.2 - Prob. 82ECh. 14.2 - Prob. 83ECh. 14.2 - Prob. 84ECh. 14.3 - In Exercises 1–22, find and .
1.
Ch. 14.3 - In Exercises 1–22, find and .
2.
Ch. 14.3 - In Exercises 1–22, find and .
3.
Ch. 14.3 - In Exercises 1–22, find and .
4.
Ch. 14.3 - In Exercises 1–22, find and .
5.
Ch. 14.3 - In Exercises 1–22, find and .
6.
Ch. 14.3 - In Exercises 1–22, find and .
7.
Ch. 14.3 - In Exercises 1–22, find and .
8.
Ch. 14.3 - In Exercises 1–22, find and .
9.
Ch. 14.3 - In Exercises 1–22, find and .
10.
Ch. 14.3 - In Exercises 1–22, find and .
11.
Ch. 14.3 - In Exercises 1–22, find and .
12.
Ch. 14.3 - In Exercises 1–22, find and .
13.
Ch. 14.3 - In Exercises 1–22, find and .
14.
Ch. 14.3 - In Exercises 1–22, find and .
15.
Ch. 14.3 - In Exercises 1–22, find and .
16.
Ch. 14.3 - In Exercises 1–22, find and .
17.
Ch. 14.3 - In Exercises 1–22, find and .
18.
Ch. 14.3 - In Exercises 1–22, find and .
19.
Ch. 14.3 - In Exercises 1–22, find and .
20.
Ch. 14.3 - Prob. 21ECh. 14.3 - Prob. 22ECh. 14.3 - In Exercises 23–34, find fx, fy, and fz.
23. f(x,...Ch. 14.3 - Prob. 24ECh. 14.3 - In Exercises 23–34, find fx, fy, and fz.
25.
Ch. 14.3 - Prob. 26ECh. 14.3 - Prob. 27ECh. 14.3 - Prob. 28ECh. 14.3 - Prob. 29ECh. 14.3 - In Exercises 23–34, find fx, fy, and fz.
30. f(x,...Ch. 14.3 - Prob. 31ECh. 14.3 - Prob. 32ECh. 14.3 - Prob. 33ECh. 14.3 - Prob. 34ECh. 14.3 - Prob. 35ECh. 14.3 - Prob. 36ECh. 14.3 - Prob. 37ECh. 14.3 - Prob. 38ECh. 14.3 - Prob. 39ECh. 14.3 - Prob. 40ECh. 14.3 - Prob. 41ECh. 14.3 - Prob. 42ECh. 14.3 - Find all the second-order partial derivatives of...Ch. 14.3 - Prob. 44ECh. 14.3 - Prob. 45ECh. 14.3 - Prob. 46ECh. 14.3 - Prob. 47ECh. 14.3 - Prob. 48ECh. 14.3 - Prob. 49ECh. 14.3 - Prob. 50ECh. 14.3 - Find all the second-order partial derivatives of...Ch. 14.3 - Prob. 52ECh. 14.3 - Find all the second-order partial derivatives of...Ch. 14.3 - Prob. 54ECh. 14.3 - In Exercises 55–60, verify that .
55.
Ch. 14.3 - Prob. 56ECh. 14.3 - In Exercises 55–60, verify that .
57.
Ch. 14.3 - Prob. 58ECh. 14.3 - Prob. 59ECh. 14.3 - Prob. 60ECh. 14.3 - Prob. 61ECh. 14.3 - Prob. 62ECh. 14.3 - Prob. 63ECh. 14.3 - Prob. 64ECh. 14.3 - Prob. 65ECh. 14.3 - Prob. 66ECh. 14.3 - Prob. 67ECh. 14.3 - Let f(x, y) = x2 + y3. Find the slope of the line...Ch. 14.3 - Prob. 69ECh. 14.3 - Prob. 70ECh. 14.3 - Prob. 71ECh. 14.3 - Prob. 72ECh. 14.3 - Prob. 73ECh. 14.3 - Prob. 74ECh. 14.3 - Prob. 75ECh. 14.3 - Prob. 76ECh. 14.3 - Prob. 77ECh. 14.3 - Prob. 78ECh. 14.3 - Prob. 79ECh. 14.3 - Prob. 80ECh. 14.3 - Prob. 81ECh. 14.3 - Prob. 82ECh. 14.3 - Prob. 83ECh. 14.3 - Prob. 84ECh. 14.3 - Prob. 85ECh. 14.3 - Show that each function in Exercises 83-90...Ch. 14.3 - Prob. 87ECh. 14.3 - Prob. 88ECh. 14.3 - Prob. 89ECh. 14.3 - Prob. 90ECh. 14.3 - Prob. 91ECh. 14.3 - Prob. 92ECh. 14.3 - Prob. 93ECh. 14.3 - Prob. 94ECh. 14.3 - Prob. 95ECh. 14.3 - Prob. 96ECh. 14.3 - Prob. 97ECh. 14.3 - Prob. 98ECh. 14.3 - Prob. 99ECh. 14.3 - The heat equation An important partial...Ch. 14.3 - Prob. 101ECh. 14.3 - Prob. 102ECh. 14.3 - Prob. 103ECh. 14.3 - Prob. 104ECh. 14.4 - In Exercises 1–6, (a) express dw/dt as a function...Ch. 14.4 - Prob. 2ECh. 14.4 - In Exercises 1–6, (a) express dw/dt as a function...Ch. 14.4 - In Exercises 1–6, (a) express dw/dt as a function...Ch. 14.4 - Prob. 5ECh. 14.4 - Prob. 6ECh. 14.4 - Prob. 7ECh. 14.4 - Prob. 8ECh. 14.4 - Prob. 9ECh. 14.4 - In Exercises 9 and 10, (a) express and as...Ch. 14.4 - Prob. 11ECh. 14.4 - Prob. 12ECh. 14.4 - Prob. 13ECh. 14.4 - Prob. 14ECh. 14.4 - Prob. 15ECh. 14.4 - Prob. 16ECh. 14.4 - Prob. 17ECh. 14.4 - Prob. 18ECh. 14.4 - Prob. 19ECh. 14.4 - Prob. 20ECh. 14.4 - Prob. 21ECh. 14.4 - Prob. 22ECh. 14.4 - Prob. 23ECh. 14.4 - Prob. 24ECh. 14.4 - Prob. 25ECh. 14.4 - Prob. 26ECh. 14.4 - Prob. 27ECh. 14.4 - Prob. 28ECh. 14.4 - Prob. 29ECh. 14.4 - Prob. 30ECh. 14.4 - Find the values of ∂z/∂x and ∂z/∂y at the points...Ch. 14.4 - Find the values of ∂z/∂x and ∂z/∂y at the points...Ch. 14.4 - Prob. 33ECh. 14.4 - Prob. 34ECh. 14.4 - Prob. 35ECh. 14.4 - Prob. 36ECh. 14.4 - Prob. 37ECh. 14.4 - Prob. 38ECh. 14.4 - Prob. 39ECh. 14.4 - Prob. 40ECh. 14.4 - Prob. 41ECh. 14.4 - Prob. 42ECh. 14.4 - Assume that z = f(x, y), x = g(t), y = h(t), fx(2,...Ch. 14.4 - Prob. 44ECh. 14.4 - Prob. 45ECh. 14.4 - Assume that z = ln (f(w)), w = g(x, y), , and y =...Ch. 14.4 - Prob. 47ECh. 14.4 - Prob. 48ECh. 14.4 - Prob. 49ECh. 14.4 - Prob. 50ECh. 14.4 - Laplace equations Show that if satisfies the...Ch. 14.4 - Prob. 52ECh. 14.4 - Prob. 53ECh. 14.4 - A space curve Let w = x2e2y cos 3z. Find the value...Ch. 14.4 - Prob. 55ECh. 14.4 - Prob. 56ECh. 14.4 - Prob. 57ECh. 14.4 - Prob. 58ECh. 14.4 - Prob. 59ECh. 14.4 - Prob. 60ECh. 14.5 - In Exercises 1–6, find the gradient of the...Ch. 14.5 - In Exercises 1–6, find the gradient of the...Ch. 14.5 - In Exercises 1–6, find the gradient of the...Ch. 14.5 - Prob. 4ECh. 14.5 - In Exercises 1–6, find the gradient of the...Ch. 14.5 - Prob. 6ECh. 14.5 - In Exercises 7–10, find f at the given point.
7.
Ch. 14.5 - In Exercises 7–10, find f at the given point.
8.
Ch. 14.5 - In Exercises 7–10, find f at the given point.
9.
Ch. 14.5 - In Exercises 7–10, find f at the given point.
10....Ch. 14.5 - In Exercises 11–18, find the derivative of the...Ch. 14.5 - In Exercises 11-18, find the derivative of the...Ch. 14.5 - Prob. 13ECh. 14.5 - Prob. 14ECh. 14.5 - Prob. 15ECh. 14.5 - In Exercises 11-18, find the derivative of the...Ch. 14.5 - Prob. 17ECh. 14.5 - In Exercises 11-18, find the derivative of the...Ch. 14.5 - In Exercises 19–24, find the directions in which...Ch. 14.5 - In Exercises 19–24, find the directions in which...Ch. 14.5 - Prob. 21ECh. 14.5 - In Exercises 19–24, find the directions in which...Ch. 14.5 - Prob. 23ECh. 14.5 - In Exercises 19–24, find the directions in which...Ch. 14.5 - Prob. 25ECh. 14.5 - In Exercises 25–28, sketch the curve f(x, y) = c,...Ch. 14.5 - In Exercises 25–28, sketch the curve f(x, y) = c,...Ch. 14.5 - Prob. 28ECh. 14.5 - Let f(x, y) = x2 − xy + y2 − y. Find the...Ch. 14.5 - Let Find the directions u and the values of for...Ch. 14.5 - Prob. 31ECh. 14.5 - Zero directional derivative In what directions is...Ch. 14.5 - Is there a direction u in which the rate of change...Ch. 14.5 - Changing temperature along a circle Is there a...Ch. 14.5 - Prob. 35ECh. 14.5 - The derivative of f(x, y, z) at a point P is...Ch. 14.5 - Directional derivatives and scalar components How...Ch. 14.5 - Prob. 38ECh. 14.5 - Prob. 39ECh. 14.5 - Prob. 40ECh. 14.5 - Prob. 41ECh. 14.5 - Prob. 42ECh. 14.5 - Prob. 43ECh. 14.5 - Prob. 44ECh. 14.6 - In Exercises 1–10, find equations for the
tangent...Ch. 14.6 - Prob. 2ECh. 14.6 - In Exercises 1–10, find equations for the
tangent...Ch. 14.6 - In Exercises 1–10, find equations for the
tangent...Ch. 14.6 - Prob. 5ECh. 14.6 - Prob. 6ECh. 14.6 - Prob. 7ECh. 14.6 - Prob. 8ECh. 14.6 - Prob. 9ECh. 14.6 - Prob. 10ECh. 14.6 - Prob. 11ECh. 14.6 - Prob. 12ECh. 14.6 - Prob. 13ECh. 14.6 - Prob. 14ECh. 14.6 - In Exercises 15–20, find parametric equations for...Ch. 14.6 - In Exercises 15–20, find parametric equations for...Ch. 14.6 - Prob. 17ECh. 14.6 - Prob. 18ECh. 14.6 - Prob. 19ECh. 14.6 - In Exercises 15–20, find parametric equations for...Ch. 14.6 - Prob. 21ECh. 14.6 - Prob. 22ECh. 14.6 - Prob. 23ECh. 14.6 - Prob. 24ECh. 14.6 - Prob. 25ECh. 14.6 - Changing temperature along a space curve The...Ch. 14.6 - In Exercises 27–32, find the linearization L(x, y)...Ch. 14.6 - Prob. 28ECh. 14.6 - Prob. 29ECh. 14.6 - In Exercises 27–32, find the linearization L(x, y)...Ch. 14.6 - Prob. 31ECh. 14.6 - Prob. 32ECh. 14.6 - Prob. 33ECh. 14.6 - Prob. 34ECh. 14.6 - Prob. 35ECh. 14.6 - Prob. 36ECh. 14.6 - Prob. 37ECh. 14.6 - Prob. 38ECh. 14.6 - Prob. 39ECh. 14.6 - Prob. 40ECh. 14.6 - Prob. 41ECh. 14.6 - Prob. 42ECh. 14.6 - Prob. 43ECh. 14.6 - Prob. 44ECh. 14.6 - Prob. 45ECh. 14.6 - Prob. 46ECh. 14.6 - Prob. 47ECh. 14.6 - Prob. 48ECh. 14.6 - Prob. 49ECh. 14.6 - Prob. 50ECh. 14.6 - Prob. 51ECh. 14.6 - Prob. 52ECh. 14.6 - Prob. 53ECh. 14.6 - Prob. 54ECh. 14.6 - Prob. 55ECh. 14.6 - The Wilson lot size formula The Wilson lot size...Ch. 14.6 - Prob. 57ECh. 14.6 - Change along the involute of a circle Find the...Ch. 14.6 - Prob. 59ECh. 14.6 - Prob. 60ECh. 14.6 - Prob. 61ECh. 14.7 - Prob. 1ECh. 14.7 - Prob. 2ECh. 14.7 - Prob. 3ECh. 14.7 - Prob. 4ECh. 14.7 - Prob. 5ECh. 14.7 - Prob. 6ECh. 14.7 - Find all the local maxima, local minima, and...Ch. 14.7 - Prob. 8ECh. 14.7 - Prob. 9ECh. 14.7 - Prob. 10ECh. 14.7 - Find all the local maxima, local minima, and...Ch. 14.7 - Find all the local maxima, local minima, and...Ch. 14.7 - Find all the local maxima, local minima, and...Ch. 14.7 - Find all the local maxima, local minima, and...Ch. 14.7 - Find all the local maxima, local minima, and...Ch. 14.7 - Find all the local maxima, local minima, and...Ch. 14.7 - Find all the local maxima, local minima, and...Ch. 14.7 - Find all the local maxima, local minima, and...Ch. 14.7 - Find all the local maxima, local minima, and...Ch. 14.7 - Find all the local maxima, local minima, and...Ch. 14.7 - Find all the local maxima, local minima, and...Ch. 14.7 - Find all the local maxima, local minima, and...Ch. 14.7 - Find all the local maxima, local minima, and...Ch. 14.7 - Find all the local maxima, local minima, and...Ch. 14.7 - Find all the local maxima, local minima, and...Ch. 14.7 - Find all the local maxima, local minima, and...Ch. 14.7 - Find all the local maxima, local minima, and...Ch. 14.7 - Prob. 28ECh. 14.7 - Prob. 29ECh. 14.7 - Prob. 30ECh. 14.7 - Prob. 31ECh. 14.7 - Prob. 32ECh. 14.7 - Prob. 33ECh. 14.7 - Prob. 34ECh. 14.7 - Prob. 35ECh. 14.7 - Prob. 36ECh. 14.7 - Prob. 37ECh. 14.7 - Prob. 38ECh. 14.7 - Prob. 39ECh. 14.7 - Prob. 40ECh. 14.7 - Temperatures A flat circular plate has the shape...Ch. 14.7 - Prob. 42ECh. 14.7 - Prob. 43ECh. 14.7 - Prob. 44ECh. 14.7 - Show that (0, 0) is a critical point of f(x, y) =...Ch. 14.7 - Prob. 46ECh. 14.7 - Prob. 47ECh. 14.7 - Prob. 48ECh. 14.7 - Among all the points on the graph of that lie...Ch. 14.7 - Prob. 50ECh. 14.7 - Prob. 51ECh. 14.7 - Prob. 52ECh. 14.7 - Prob. 53ECh. 14.7 - Prob. 54ECh. 14.7 - Prob. 55ECh. 14.7 - Prob. 56ECh. 14.7 - Prob. 57ECh. 14.7 - Prob. 58ECh. 14.7 - Prob. 59ECh. 14.7 - Prob. 60ECh. 14.7 - Prob. 61ECh. 14.7 - Prob. 62ECh. 14.7 - Prob. 63ECh. 14.7 - Prob. 64ECh. 14.7 - Prob. 65ECh. 14.7 - Prob. 66ECh. 14.7 - Prob. 67ECh. 14.7 - Prob. 68ECh. 14.7 - Prob. 69ECh. 14.7 - Prob. 70ECh. 14.8 - Extrema on an ellipse Find the points on the...Ch. 14.8 - Prob. 2ECh. 14.8 - Maximum on a line Find the maximum value of f(x,...Ch. 14.8 - Prob. 4ECh. 14.8 - Constrained minimum Find the points on the curve...Ch. 14.8 - Prob. 6ECh. 14.8 - Prob. 7ECh. 14.8 - Prob. 8ECh. 14.8 - Prob. 9ECh. 14.8 - Prob. 10ECh. 14.8 - Prob. 11ECh. 14.8 - Prob. 12ECh. 14.8 - Prob. 13ECh. 14.8 - Prob. 14ECh. 14.8 - Prob. 15ECh. 14.8 - Prob. 16ECh. 14.8 - Prob. 17ECh. 14.8 - Prob. 18ECh. 14.8 - Prob. 19ECh. 14.8 - Prob. 20ECh. 14.8 - Prob. 21ECh. 14.8 - Prob. 22ECh. 14.8 - Prob. 23ECh. 14.8 - Prob. 24ECh. 14.8 - Prob. 25ECh. 14.8 - Prob. 26ECh. 14.8 - Prob. 27ECh. 14.8 - Prob. 28ECh. 14.8 - Hottest point on a space probe A space probe in...Ch. 14.8 - Prob. 30ECh. 14.8 - Prob. 31ECh. 14.8 - Prob. 32ECh. 14.8 - Prob. 33ECh. 14.8 - Prob. 34ECh. 14.8 - Length of a beam In Section 4.6, Exercise 45, we...Ch. 14.8 - Locating a radio telescope You are in charge of...Ch. 14.8 - Prob. 37ECh. 14.8 - Prob. 38ECh. 14.8 - Prob. 39ECh. 14.8 - Prob. 40ECh. 14.8 - Prob. 41ECh. 14.8 - Prob. 42ECh. 14.8 - Prob. 43ECh. 14.8 - Prob. 44ECh. 14.8 - Prob. 45ECh. 14.8 - Prob. 46ECh. 14.8 - Prob. 47ECh. 14.8 - Sum of products Let a1, a2,..., an be n positive...Ch. 14.9 - In Exercises 1–10, use Taylor’s formula for f(x,...Ch. 14.9 - Prob. 2ECh. 14.9 - Prob. 3ECh. 14.9 - Prob. 4ECh. 14.9 - Prob. 5ECh. 14.9 - Prob. 6ECh. 14.9 - Prob. 7ECh. 14.9 - Prob. 8ECh. 14.9 - Prob. 9ECh. 14.9 - Prob. 10ECh. 14.9 - Prob. 11ECh. 14.9 - Use Taylor’s formula to find a quadratic...Ch. 14.10 - Prob. 1ECh. 14.10 - Prob. 2ECh. 14.10 - Prob. 3ECh. 14.10 - Prob. 4ECh. 14.10 - Prob. 5ECh. 14.10 - Prob. 6ECh. 14.10 - Prob. 7ECh. 14.10 - Prob. 8ECh. 14.10 - Prob. 9ECh. 14.10 - Prob. 10ECh. 14.10 - Prob. 11ECh. 14.10 - Prob. 12ECh. 14 - Prob. 1GYRCh. 14 - Prob. 2GYRCh. 14 - Prob. 3GYRCh. 14 - Prob. 4GYRCh. 14 - Prob. 5GYRCh. 14 - Prob. 6GYRCh. 14 - Prob. 7GYRCh. 14 - Prob. 8GYRCh. 14 - Prob. 9GYRCh. 14 - Prob. 10GYRCh. 14 - What does it mean for a function f(x, y) to be...Ch. 14 - Prob. 12GYRCh. 14 - Prob. 13GYRCh. 14 - Prob. 14GYRCh. 14 - Prob. 15GYRCh. 14 - Prob. 16GYRCh. 14 - Prob. 17GYRCh. 14 - Prob. 18GYRCh. 14 - Prob. 19GYRCh. 14 - Prob. 20GYRCh. 14 - Prob. 21GYRCh. 14 - Prob. 22GYRCh. 14 - Prob. 23GYRCh. 14 - Describe the method of Lagrange multipliers and...Ch. 14 - Prob. 25GYRCh. 14 - Prob. 26GYRCh. 14 - Prob. 1PECh. 14 - Prob. 2PECh. 14 - Prob. 3PECh. 14 - Prob. 4PECh. 14 - Prob. 5PECh. 14 - Prob. 6PECh. 14 - Prob. 7PECh. 14 - Prob. 8PECh. 14 - Prob. 9PECh. 14 - Prob. 10PECh. 14 - Prob. 11PECh. 14 - Prob. 12PECh. 14 - Prob. 13PECh. 14 - Prob. 14PECh. 14 - Prob. 15PECh. 14 - Prob. 16PECh. 14 - Prob. 17PECh. 14 - Prob. 18PECh. 14 - Prob. 19PECh. 14 - Prob. 20PECh. 14 - Prob. 21PECh. 14 - Prob. 22PECh. 14 - Prob. 23PECh. 14 - Prob. 24PECh. 14 - Prob. 25PECh. 14 - Prob. 26PECh. 14 - Prob. 27PECh. 14 - Prob. 28PECh. 14 - Prob. 29PECh. 14 - Prob. 30PECh. 14 - Prob. 31PECh. 14 - Prob. 32PECh. 14 - Prob. 33PECh. 14 - Prob. 34PECh. 14 - Prob. 35PECh. 14 - Prob. 36PECh. 14 - Prob. 37PECh. 14 - Prob. 38PECh. 14 - Prob. 39PECh. 14 - Prob. 40PECh. 14 - Prob. 41PECh. 14 - Prob. 42PECh. 14 - Prob. 43PECh. 14 - Prob. 44PECh. 14 - Prob. 45PECh. 14 - Prob. 46PECh. 14 - Prob. 47PECh. 14 - Prob. 48PECh. 14 - Prob. 49PECh. 14 - Prob. 50PECh. 14 - Prob. 51PECh. 14 - Prob. 52PECh. 14 - Prob. 53PECh. 14 - Prob. 54PECh. 14 - Prob. 55PECh. 14 - Prob. 56PECh. 14 - Prob. 57PECh. 14 - Prob. 58PECh. 14 - Prob. 59PECh. 14 - Prob. 60PECh. 14 - Change in an electrical circuit Suppose that the...Ch. 14 - Prob. 62PECh. 14 - Prob. 63PECh. 14 - Prob. 64PECh. 14 - Prob. 65PECh. 14 - Prob. 66PECh. 14 - Prob. 67PECh. 14 - Prob. 68PECh. 14 - Prob. 69PECh. 14 - Prob. 70PECh. 14 - Prob. 71PECh. 14 - Prob. 72PECh. 14 - Prob. 73PECh. 14 - Prob. 74PECh. 14 - Prob. 75PECh. 14 - Prob. 76PECh. 14 - Prob. 77PECh. 14 - Prob. 78PECh. 14 - Prob. 79PECh. 14 - Prob. 80PECh. 14 - Prob. 81PECh. 14 - Prob. 82PECh. 14 - Prob. 83PECh. 14 - Prob. 84PECh. 14 - Prob. 85PECh. 14 - Prob. 86PECh. 14 - Prob. 87PECh. 14 - Prob. 88PECh. 14 - Prob. 89PECh. 14 - Prob. 90PECh. 14 - Prob. 91PECh. 14 - Prob. 92PECh. 14 - Prob. 93PECh. 14 - Prob. 94PECh. 14 - Prob. 95PECh. 14 - Prob. 96PECh. 14 - Prob. 97PECh. 14 - Prob. 98PECh. 14 - Prob. 99PECh. 14 - Prob. 100PECh. 14 - Prob. 101PECh. 14 - Prob. 102PECh. 14 - Prob. 1AAECh. 14 - Prob. 2AAECh. 14 - Prob. 3AAECh. 14 - Prob. 4AAECh. 14 - Prob. 5AAECh. 14 - Prob. 6AAECh. 14 - Prob. 7AAECh. 14 - Prob. 8AAECh. 14 - Prob. 9AAECh. 14 - Prob. 10AAECh. 14 - Prob. 11AAECh. 14 - Prob. 12AAECh. 14 - Prob. 13AAECh. 14 - Prob. 14AAECh. 14 - Prob. 15AAECh. 14 - Prob. 16AAECh. 14 - Prob. 17AAECh. 14 - Prob. 18AAECh. 14 - Prob. 19AAECh. 14 - Velocity after a ricochet A particle traveling in...Ch. 14 - Prob. 21AAECh. 14 - Prob. 22AAECh. 14 - Prob. 23AAECh. 14 - Prob. 24AAE
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- (10) (16 points) Let R>0. Consider the truncated sphere S given as x² + y² + (z = √15R)² = R², z ≥0. where F(x, y, z) = −yi + xj . (a) (8 points) Consider the vector field V (x, y, z) = (▼ × F)(x, y, z) Think of S as a hot-air balloon where the vector field V is the velocity vector field measuring the hot gasses escaping through the porous surface S. The flux of V across S gives the volume flow rate of the gasses through S. Calculate this flux. Hint: Parametrize the boundary OS. Then use Stokes' Theorem. (b) (8 points) Calculate the surface area of the balloon. To calculate the surface area, do the following: Translate the balloon surface S by the vector (-15)k. The translated surface, call it S+ is part of the sphere x² + y²+z² = R². Why do S and S+ have the same area? ⚫ Calculate the area of S+. What is the natural spherical parametrization of S+?arrow_forward(1) (8 points) Let c(t) = (et, et sint, et cost). Reparametrize c as a unit speed curve starting from the point (1,0,1).arrow_forward(9) (16 points) Let F(x, y, z) = (x² + y − 4)i + 3xyj + (2x2 +z²)k = - = (x²+y4,3xy, 2x2 + 2²). (a) (4 points) Calculate the divergence and curl of F. (b) (6 points) Find the flux of V x F across the surface S given by x² + y²+2² = 16, z ≥ 0. (c) (6 points) Find the flux of F across the boundary of the unit cube E = [0,1] × [0,1] x [0,1].arrow_forward
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