Study Guide for Stewart's Multivariable Calculus, 8th
8th Edition
ISBN: 9781305271845
Author: Stewart, James
Publisher: Brooks Cole
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Chapter 16.1, Problem 4PT
True or False:
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(3) (20 points) Let F(x, y, z) = (y, z, x²z). Define
E = {(x, y, z) | x² + y² ≤ z ≤ 1, x ≤ 0}.
(a) (2 points) Calculate the divergence V. F.
(b) (4 points) Let D = {(x, y) | x² + y² ≤ 1, x ≤ 0} Without calculation, show that
the triple integral
√ (V · F) dV = √ 2²(1.
= x²(1 − x² - y²) dA.
E
(2) (22 points) Let F(x, y, z) = (x sin y, cos y, ―xy).
(a) (2 points) Calculate V. F.
(b) (6 points) Given a vector field
is everywhere defined with V
G₁(x, y, z) = *
G2(x, y, z) = −
G3(x, y, z) = 0.
0
0
F(x, y, z) = (F₁(x, y, z), F₂(x, y, z), F(x, y, z)) that
F = 0, let G = (G1, G2, G3) where
F₂(x,
y,
y, t) dt
- √ F³(x, t, 0) dt,
*
F1(x,
y, t) dt,
t) dt - √ F
Calculate G for the vector field F(x, y, z) = (x sin y, cos y, -xy).
Evaluate the following integral over the Region R.
(Answer accurate to 2 decimal places).
√ √(x + y) A
R
R = {(x, y) | 25 < x² + y² ≤ 36, x < 0}
Hint: The integral and Region is defined in rectangular coordinates.
Chapter 16 Solutions
Study Guide for Stewart's Multivariable Calculus, 8th
Ch. 16.1 - For F(x,y)=(x+y)i+(2x4y)j, which vector, a, b, c,...Ch. 16.1 - Prob. 2PTCh. 16.1 - Prob. 3PTCh. 16.1 - True or False: F(x,y)=2yi+2xj is conservative.Ch. 16.2 - A definite integral for C(x+y)ds, where C is the...Ch. 16.2 - True or False: The curve at the right appears to...Ch. 16.2 - A definite integral for CFdr, where F(x,y)=x2i+y2j...Ch. 16.2 - Prob. 4PTCh. 16.2 - Prob. 5PTCh. 16.3 - Prob. 1PT
Ch. 16.3 - Which curve is simple but not closed?Ch. 16.3 - Prob. 3PTCh. 16.3 - Prob. 4PTCh. 16.3 - Prob. 5PTCh. 16.4 - Prob. 1PTCh. 16.4 - Prob. 2PTCh. 16.4 - Prob. 3PTCh. 16.4 - Prob. 4PTCh. 16.5 - Prob. 1PTCh. 16.5 - Prob. 2PTCh. 16.5 - Prob. 3PTCh. 16.5 - True or False: div curl F = 0.Ch. 16.5 - Prob. 5PTCh. 16.5 - Prob. 6PTCh. 16.6 - Prob. 1PTCh. 16.6 - Prob. 2PTCh. 16.6 - Prob. 3PTCh. 16.6 - Prob. 4PTCh. 16.6 - Write an iterated integral for the area of that...Ch. 16.7 - Prob. 1PTCh. 16.7 - Prob. 2PTCh. 16.7 - Prob. 3PTCh. 16.8 - Prob. 1PTCh. 16.8 - Prob. 2PTCh. 16.8 - Let F(x, y, z) = zi + xj yk and the curve C be...Ch. 16.9 - Prob. 1PTCh. 16.9 - Prob. 2PT
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