Study Guide for Stewart's Multivariable Calculus, 8th
8th Edition
ISBN: 9781305271845
Author: Stewart, James
Publisher: Brooks Cole
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Chapter 15.2, Problem 2PT
To determine
Whether the statement “
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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 15 Solutions
Study Guide for Stewart's Multivariable Calculus, 8th
Ch. 15.1 - Prob. 1PTCh. 15.1 - Prob. 2PTCh. 15.1 - Let R={(x,y)|3x5,2y4}andf(x,y)=y2x2.For every...Ch. 15.1 - Sometimes, Always, or Never: Rf(x,y)dA is the...Ch. 15.1 - Prob. 5PTCh. 15.1 - Prob. 6PTCh. 15.1 - Prob. 7PTCh. 15.1 - Prob. 8PTCh. 15.2 - Prob. 1PTCh. 15.2 - Prob. 2PT
Ch. 15.2 - Prob. 3PTCh. 15.2 - Prob. 4PTCh. 15.3 - Prob. 1PTCh. 15.3 - Prob. 2PTCh. 15.4 - Prob. 1PTCh. 15.4 - Prob. 2PTCh. 15.4 - Prob. 3PTCh. 15.4 - True or False: For f(x, y) = x2(x + y), x and y...Ch. 15.5 - Prob. 1PTCh. 15.6 - Prob. 1PTCh. 15.6 - Prob. 2PTCh. 15.6 - EzdV, where E is the wedge-shaped solid shown at...Ch. 15.6 - Prob. 4PTCh. 15.7 - Prob. 1PTCh. 15.7 - Prob. 2PTCh. 15.7 - Prob. 3PTCh. 15.7 - Prob. 4PTCh. 15.8 - Prob. 1PTCh. 15.8 - Prob. 2PTCh. 15.8 - Prob. 3PTCh. 15.8 - Prob. 4PTCh. 15.9 - Find the Jacobian for x = u2v2, y = u2 + v2. a)...Ch. 15.9 - Find the iterated integral for RdA, where R is the...
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- A driver is traveling along a straight road when a buffalo runs into the street. This driver has a reaction time of 0.75 seconds. When the driver sees the buffalo he is traveling at 44 ft/s, his car can decelerate at 2 ft/s^2 when the brakes are applied. What is the stopping distance between when the driver first saw the buffalo, to when the car stops.arrow_forwardTopic 2 Evaluate S x dx, using u-substitution. Then find the integral using 1-x2 trigonometric substitution. Discuss the results! Topic 3 Explain what an elementary anti-derivative is. Then consider the following ex integrals: fed dx x 1 Sdx In x Joseph Liouville proved that the first integral does not have an elementary anti- derivative Use this fact to prove that the second integral does not have an elementary anti-derivative. (hint: use an appropriate u-substitution!)arrow_forward1. Given the vector field F(x, y, z) = -xi, verify the relation 1 V.F(0,0,0) = lim 0+ volume inside Se ff F• Nds SE where SE is the surface enclosing a cube centred at the origin and having edges of length 2€. Then, determine if the origin is sink or source.arrow_forward
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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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