Single Variable Calculus: Early Transcendentals
8th Edition
ISBN: 9781305270336
Author: James Stewart
Publisher: Cengage Learning
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Chapter B, Problem 48E
To determine
To sketch: The region in the xy-plane.
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(10 points) Let f(x, y, z) = ze²²+y². Let
E = {(x, y, z) | x² + y² ≤ 4,2 ≤ z ≤ 3}.
Calculate the integral
f(x, y, z) dv.
E
(12 points) Let
E={(x, y, z)|x²+ y² + z² ≤ 4, x, y, z > 0}.
(a) (4 points) Describe the region E using spherical coordinates, that is, find p, 0, and such
that
(x, y, z) (psin cos 0, psin sin 0, p cos) € E.
(b) (8 points) Calculate the integral
E
xyz dV using spherical coordinates.
(10 points) Let f(x, y, z) = ze²²+y². Let
E = {(x, y, z) | x² + y² ≤ 4,2 ≤ z < 3}.
Calculate the integral
y,
f(x, y, z) dV.
Chapter B Solutions
Single Variable Calculus: Early Transcendentals
Ch. B - Prob. 1ECh. B - Prob. 2ECh. B - Prob. 3ECh. B - Prob. 4ECh. B - Prob. 5ECh. B - Prob. 6ECh. B - Prob. 7ECh. B - Prob. 8ECh. B - Prob. 9ECh. B - Prob. 10E
Ch. B - Show that the triangle with vertices A(0, 2), B(3,...Ch. B - (a) Show that the triangle with vertices A(6, 7),...Ch. B - Prob. 13ECh. B - (a) Show that the points A(1, 3), B(3, 11), and...Ch. B - Show that A(1, 1), B(7, 4), C(5, 10), and D(1, 7)...Ch. B - Prob. 16ECh. B - Prob. 17ECh. B - Prob. 18ECh. B - Prob. 19ECh. B - Prob. 20ECh. B - Prob. 21ECh. B - Prob. 22ECh. B - Prob. 23ECh. B - Prob. 24ECh. B - Find an equation of the line that satisfies the...Ch. B - Prob. 26ECh. B - Prob. 27ECh. B - Prob. 28ECh. B - Prob. 29ECh. B - Find an equation of the line that satisfies the...Ch. B - Prob. 31ECh. B - Prob. 32ECh. B - Prob. 33ECh. B - Prob. 34ECh. B - Prob. 35ECh. B - Prob. 36ECh. B - Prob. 37ECh. B - Prob. 38ECh. B - Prob. 39ECh. B - Prob. 40ECh. B - Prob. 41ECh. B - Prob. 42ECh. B - Prob. 43ECh. B - Prob. 44ECh. B - Prob. 45ECh. B - Prob. 46ECh. B - Prob. 47ECh. B - Prob. 48ECh. B - Prob. 49ECh. B - Prob. 50ECh. B - Prob. 51ECh. B - Prob. 52ECh. B - Prob. 53ECh. B - Prob. 54ECh. B - Find the midpoint of the line segment joining the...Ch. B - Prob. 56ECh. B - Prob. 57ECh. B - Show that the lines 3x 5y + 19 = 0 and 10x + 6y ...Ch. B - Prob. 59ECh. B - Prob. 60ECh. B - Prob. 61ECh. B - Prob. 62E
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