CALCULUS+ITS...,EXP.(LL)-W/CODE NVCC
19th Edition
ISBN: 9780136572671
Author: BITTINGER
Publisher: PEARSON C
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Chapter B, Problem 20E
To determine
To find:
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(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 B Solutions
CALCULUS+ITS...,EXP.(LL)-W/CODE NVCC
Ch. B - Prob. 1ECh. B - Evaluate each limit. Use lHĂ´pitals Rule when...Ch. B - Prob. 3ECh. B - Prob. 4ECh. B - Prob. 5ECh. B - Prob. 6ECh. B - Prob. 7ECh. B - Prob. 8ECh. B - Evaluate each limit. Use lHĂ´pitals Rule when...Ch. B - Evaluate each limit. Use lHĂ´pitals Rule when...
Ch. B - Evaluate each limit. Use lHĂ´pitals Rule when...Ch. B - Prob. 12ECh. B - Prob. 13ECh. B - Prob. 14ECh. B - Prob. 15ECh. B - Prob. 16ECh. B - Evaluate each limit. Use lHĂ´pitals Rule when...Ch. B - Evaluate each limit. Use lHĂ´pitals Rule when...Ch. B - Evaluate each limit. Use lHĂ´pitals Rule when...Ch. B - Prob. 20ECh. B - Prob. 21ECh. B - Prob. 22ECh. B - Prob. 23ECh. B - Prob. 24ECh. B - Evaluate each limit. Use lHĂ´pitals Rule when...Ch. B - Evaluate each limit. Use lHĂ´pitals Rule when...Ch. B - Prob. 27ECh. B - Prob. 28ECh. B - Prob. 29ECh. B - Prob. 30ECh. B - Prob. 31ECh. B - Evaluate limx1x26xxCh. B - Evaluate limxx24xxx2+10xxCh. B - Prob. 34ECh. B - Prob. 35ECh. B - Prob. 38E
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