Single Variable Calculus: Early Transcendentals, Volume I
8th Edition
ISBN: 9781305270343
Author: James Stewart
Publisher: Cengage Learning
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Chapter E, Problem 42E
To determine
To prove: The generalized triangle inequality
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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 E Solutions
Single Variable Calculus: Early Transcendentals, Volume I
Ch. E - Write the sum in expanded form. 1. i=15iCh. E - Prob. 2ECh. E - Prob. 3ECh. E - Write the sum in expanded form. 4. i=46i3Ch. E - Prob. 5ECh. E - Prob. 6ECh. E - Prob. 7ECh. E - Prob. 8ECh. E - Prob. 9ECh. E - Write the sum in expanded form. 10. i=1nf(xi)xi
Ch. E - Prob. 11ECh. E - Prob. 12ECh. E - Prob. 13ECh. E - Prob. 14ECh. E - Prob. 15ECh. E - Prob. 16ECh. E - Prob. 17ECh. E - Prob. 18ECh. E - Prob. 19ECh. E - Prob. 20ECh. E - Prob. 21ECh. E - Prob. 22ECh. E - Prob. 23ECh. E - Prob. 24ECh. E - Prob. 25ECh. E - Prob. 26ECh. E - Prob. 27ECh. E - Prob. 28ECh. E - Prob. 29ECh. E - Prob. 30ECh. E - Prob. 31ECh. E - Prob. 32ECh. E - Prob. 33ECh. E - Prob. 34ECh. E - Prob. 35ECh. E - Find the number n such that i=1ni=78.Ch. E - Prob. 37ECh. E - Prob. 38ECh. E - Prob. 39ECh. E - Prove formula (e) of Theorem 3 using the following...Ch. E - Prob. 41ECh. E - Prob. 42ECh. E - Prob. 43ECh. E - Prob. 44ECh. E - Prob. 45ECh. E - Find the limit. 46. limni=1n3n[(1+3in)32(1+3in)]Ch. E - Prob. 47ECh. E - Prob. 48ECh. E - Prob. 49ECh. E - Prob. 50E
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