Study Guide for Stewart's Multivariable Calculus, 8th
8th Edition
ISBN: 9781305271845
Author: Stewart, James
Publisher: Brooks Cole
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Chapter 16.3, Problem 5PT
To determine
To choose: The appropriate option for the statement “Let C be the line from
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3.1 Limits
1. If lim f(x)=-6 and lim f(x)=5, then lim f(x). Explain your choice.
x+3°
x+3*
x+3
(a) Is 5
(c) Does not exist
(b) is 6
(d) is infinite
1 pts
Let F and G be vector fields such that ▼ × F(0, 0, 0) = (0.76, -9.78, 3.29), G(0, 0, 0) = (−3.99, 6.15, 2.94), and
G is irrotational. Then sin(5V (F × G)) at (0, 0, 0) is
Question 1
-0.246
0.072
-0.934
0.478
-0.914
-0.855
0.710
0.262
.
2. Answer the following questions.
(A) [50%] Given the vector field F(x, y, z) = (x²y, e", yz²), verify the differential identity
Vx (VF) V(V •F) - V²F
(B) [50%] Remark. You are confined to use the differential identities.
Let u and v be scalar fields, and F be a vector field given by
F = (Vu) x (Vv)
(i) Show that F is solenoidal (or incompressible).
(ii) Show that
G =
(uvv – vVu)
is a vector potential for F.
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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- Question 2 Let F be a solenoidal vector field, suppose V × F = (-8xy + 12z², −9x² + 4y² + 9z², 6y²), and let (P,Q,R) = V²F(.725, —.283, 1.73). Then the value of sin(2P) + sin(3Q) + sin(4R) is -2.024 1.391 0.186 -0.994 -2.053 -0.647 -0.588 -1.851 1 ptsarrow_forward1 pts Let F and G be vector fields such that ▼ × F(0, 0, 0) = (0.76, -9.78, 3.29), G(0, 0, 0) = (−3.99, 6.15, 2.94), and G is irrotational. Then sin(5V (F × G)) at (0, 0, 0) is Question 1 -0.246 0.072 -0.934 0.478 -0.914 -0.855 0.710 0.262 .arrow_forwardanswerarrow_forward
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