Student Solutions Manual for Stewart's Single Variable Calculus: Early Transcendentals, 8th (James Stewart Calculus)
8th Edition
ISBN: 9781305272422
Author: James Stewart, Jeffrey A. Cole, Daniel Drucker, Daniel Anderson
Publisher: Cengage Learning
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Chapter E, Problem 5E
To determine
To write: The sum
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Students have asked these similar questions
(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.
(14 points) Let f: R3 R and T: R3.
→R³ be defined by
f(x, y, z) = ln(x²+ y²+2²),
T(p, 0,4)=(psin cos 0, psin sin, pcos).
(a) (4 points) Write out the composition g(p, 0, 4) = (foT)(p,, ) explicitly. Then calculate the
gradient Vg directly, i.e. without using the chain rule.
(b) (4 points) Calculate the gradient Vf(x, y, z) where (x, y, z) = T(p, 0,4).
(c) (6 points) Calculate the derivative matrix DT(p, 0, p). Then use the Chain Rule to calculate
Vg(r,0,4).
Chapter E Solutions
Student Solutions Manual for Stewart's Single Variable Calculus: Early Transcendentals, 8th (James Stewart Calculus)
Ch. E - Prob. 1ECh. E - Write the sum in expanded form. 2. i=161i+1Ch. 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 - Write the sum in expanded form. 9. j=0n1(1)jCh. E - Write the sum in expanded form. 10. i=1nf(xi)xi
Ch. E - Prob. 11ECh. E - Write the sum in sigma notation. 12. 3+4+5+6+7Ch. E - Prob. 13ECh. E - Write the sum in sigma notation. 14....Ch. 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 - Find the value of the sum. 26. i=11004Ch. E - Prob. 27ECh. E - Prob. 28ECh. E - Prob. 29ECh. E - Prob. 30ECh. E - Find the value of the sum. 31. i=1n(i2+3i+4)Ch. E - Prob. 32ECh. E - Prob. 33ECh. E - Prob. 34ECh. E - Prob. 35ECh. E - Prob. 36ECh. E - Prob. 37ECh. E - Prob. 38ECh. E - Prob. 39ECh. E - Prove formula (e) of Theorem 3 using the following...Ch. E - Evaluate each telescoping sum. (a) i=1n[i4(i1)4]...Ch. E - Prob. 42ECh. E - Prob. 43ECh. E - Prob. 44ECh. E - Prob. 45ECh. E - Prob. 46ECh. E - Prob. 47ECh. E - Prob. 48ECh. E - Prob. 49ECh. E - Prob. 50E
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