Applied Calculus, 6e WileyPLUS + Loose-leaf
6th Edition
ISBN: 9781119408901
Author: Deborah Hughes-Hallett, Andrew M. Gleason, Patti Frazer Lock, Daniel E. Flath
Publisher: Wiley (WileyPLUS Products)
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Chapter 4.4, Problem 5P
To determine
(a)
To explain:
The significance of the points
To determine
(b)
To explain:
The reason for one point is
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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 4 Solutions
Applied Calculus, 6e WileyPLUS + Loose-leaf
Ch. 4.1 - Prob. 1PCh. 4.1 - Prob. 2PCh. 4.1 - Prob. 3PCh. 4.1 - Prob. 4PCh. 4.1 - Prob. 5PCh. 4.1 - Prob. 6PCh. 4.1 - Prob. 7PCh. 4.1 - Prob. 8PCh. 4.1 - Prob. 9PCh. 4.1 - Prob. 10P
Ch. 4.1 - Prob. 11PCh. 4.1 - Prob. 12PCh. 4.1 - Prob. 13PCh. 4.1 - Prob. 14PCh. 4.1 - Prob. 15PCh. 4.1 - Prob. 16PCh. 4.1 - Prob. 17PCh. 4.1 - Prob. 18PCh. 4.1 - Prob. 19PCh. 4.1 - Prob. 20PCh. 4.1 - Prob. 21PCh. 4.1 - Prob. 22PCh. 4.1 - Prob. 23PCh. 4.1 - Prob. 24PCh. 4.1 - Prob. 25PCh. 4.1 - Prob. 26PCh. 4.1 - Prob. 27PCh. 4.1 - Prob. 28PCh. 4.1 - Prob. 29PCh. 4.1 - Prob. 30PCh. 4.1 - Prob. 31PCh. 4.1 - Prob. 32PCh. 4.1 - Prob. 33PCh. 4.1 - Prob. 34PCh. 4.1 - Prob. 35PCh. 4.1 - Prob. 36PCh. 4.1 - Prob. 37PCh. 4.1 - Prob. 38PCh. 4.1 - Prob. 39PCh. 4.1 - Prob. 40PCh. 4.1 - Prob. 41PCh. 4.1 - Prob. 42PCh. 4.1 - Prob. 43PCh. 4.1 - Prob. 44PCh. 4.1 - Prob. 45PCh. 4.1 - Prob. 46PCh. 4.1 - Prob. 47PCh. 4.1 - Prob. 48PCh. 4.1 - Prob. 49PCh. 4.1 - Prob. 50PCh. 4.1 - Prob. 51PCh. 4.1 - Prob. 52PCh. 4.1 - Prob. 53PCh. 4.1 - Prob. 54PCh. 4.1 - Prob. 55PCh. 4.1 - Prob. 56PCh. 4.1 - Prob. 57PCh. 4.1 - Prob. 58PCh. 4.2 - Prob. 1PCh. 4.2 - Prob. 2PCh. 4.2 - Prob. 3PCh. 4.2 - Prob. 4PCh. 4.2 - Prob. 5PCh. 4.2 - Prob. 6PCh. 4.2 - Prob. 7PCh. 4.2 - Prob. 8PCh. 4.2 - Prob. 9PCh. 4.2 - Prob. 10PCh. 4.2 - Prob. 11PCh. 4.2 - Prob. 12PCh. 4.2 - Prob. 13PCh. 4.2 - Prob. 14PCh. 4.2 - Prob. 15PCh. 4.2 - Prob. 16PCh. 4.2 - Prob. 17PCh. 4.2 - Prob. 18PCh. 4.2 - Prob. 19PCh. 4.2 - Prob. 20PCh. 4.2 - Prob. 21PCh. 4.2 - Prob. 22PCh. 4.2 - Prob. 23PCh. 4.2 - Prob. 24PCh. 4.2 - Prob. 25PCh. 4.2 - Prob. 26PCh. 4.2 - Prob. 27PCh. 4.2 - Prob. 28PCh. 4.2 - Prob. 29PCh. 4.2 - Prob. 30PCh. 4.2 - Prob. 31PCh. 4.2 - Prob. 32PCh. 4.2 - Prob. 33PCh. 4.2 - Prob. 34PCh. 4.2 - Prob. 35PCh. 4.2 - Prob. 36PCh. 4.2 - Prob. 37PCh. 4.2 - Prob. 38PCh. 4.2 - Prob. 39PCh. 4.2 - Prob. 40PCh. 4.2 - Prob. 41PCh. 4.3 - Prob. 1PCh. 4.3 - Prob. 2PCh. 4.3 - Prob. 3PCh. 4.3 - Prob. 4PCh. 4.3 - Prob. 5PCh. 4.3 - Prob. 6PCh. 4.3 - Prob. 7PCh. 4.3 - Prob. 8PCh. 4.3 - Prob. 9PCh. 4.3 - Prob. 10PCh. 4.3 - Prob. 11PCh. 4.3 - Prob. 12PCh. 4.3 - Prob. 13PCh. 4.3 - Prob. 14PCh. 4.3 - Prob. 15PCh. 4.3 - Prob. 16PCh. 4.3 - Prob. 17PCh. 4.3 - Prob. 18PCh. 4.3 - Prob. 19PCh. 4.3 - Prob. 20PCh. 4.3 - Prob. 21PCh. 4.3 - Prob. 22PCh. 4.3 - Prob. 23PCh. 4.3 - Prob. 24PCh. 4.3 - Prob. 25PCh. 4.3 - Prob. 26PCh. 4.3 - Prob. 27PCh. 4.3 - Prob. 28PCh. 4.3 - Prob. 29PCh. 4.3 - Prob. 30PCh. 4.3 - Prob. 31PCh. 4.3 - Prob. 32PCh. 4.3 - Prob. 33PCh. 4.3 - Prob. 34PCh. 4.3 - Prob. 35PCh. 4.3 - Prob. 36PCh. 4.3 - Prob. 37PCh. 4.3 - Prob. 38PCh. 4.3 - Prob. 39PCh. 4.3 - Prob. 40PCh. 4.3 - Prob. 41PCh. 4.3 - Prob. 42PCh. 4.3 - Prob. 43PCh. 4.3 - Prob. 44PCh. 4.3 - Prob. 45PCh. 4.3 - Prob. 46PCh. 4.3 - Prob. 47PCh. 4.3 - Prob. 48PCh. 4.3 - Prob. 49PCh. 4.3 - Prob. 50PCh. 4.3 - Prob. 51PCh. 4.3 - Prob. 52PCh. 4.3 - Prob. 53PCh. 4.3 - Prob. 54PCh. 4.3 - Prob. 55PCh. 4.3 - Prob. 56PCh. 4.3 - Prob. 57PCh. 4.3 - Prob. 58PCh. 4.3 - Prob. 59PCh. 4.3 - Prob. 60PCh. 4.4 - Prob. 1PCh. 4.4 - Prob. 2PCh. 4.4 - Prob. 3PCh. 4.4 - Prob. 4PCh. 4.4 - Prob. 5PCh. 4.4 - Prob. 6PCh. 4.4 - Prob. 7PCh. 4.4 - Prob. 8PCh. 4.4 - Prob. 9PCh. 4.4 - Prob. 10PCh. 4.4 - Prob. 11PCh. 4.4 - Prob. 12PCh. 4.4 - 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Prob. 1SYUCh. 4 - Prob. 2SYUCh. 4 - Prob. 3SYUCh. 4 - Prob. 4SYUCh. 4 - Prob. 5SYUCh. 4 - Prob. 6SYUCh. 4 - Prob. 7SYUCh. 4 - Prob. 8SYUCh. 4 - Prob. 9SYUCh. 4 - Prob. 10SYUCh. 4 - Prob. 11SYUCh. 4 - Prob. 12SYUCh. 4 - Prob. 13SYUCh. 4 - Prob. 14SYUCh. 4 - Prob. 15SYUCh. 4 - Prob. 16SYUCh. 4 - Prob. 17SYUCh. 4 - Prob. 18SYUCh. 4 - Prob. 19SYUCh. 4 - Prob. 20SYUCh. 4 - Prob. 21SYUCh. 4 - Prob. 22SYUCh. 4 - Prob. 23SYUCh. 4 - Prob. 24SYUCh. 4 - Prob. 25SYUCh. 4 - Prob. 26SYUCh. 4 - Prob. 27SYUCh. 4 - Prob. 28SYUCh. 4 - Prob. 29SYUCh. 4 - Prob. 30SYUCh. 4 - Prob. 31SYUCh. 4 - Prob. 32SYUCh. 4 - Prob. 33SYUCh. 4 - Prob. 34SYUCh. 4 - Prob. 35SYUCh. 4 - Prob. 36SYUCh. 4 - Prob. 37SYUCh. 4 - Prob. 38SYUCh. 4 - Prob. 39SYUCh. 4 - Prob. 40SYUCh. 4 - Prob. 41SYUCh. 4 - Prob. 42SYUCh. 4 - Prob. 43SYUCh. 4 - Prob. 44SYUCh. 4 - Prob. 45SYUCh. 4 - Prob. 46SYUCh. 4 - Prob. 47SYUCh. 4 - Prob. 48SYUCh. 4 - Prob. 49SYUCh. 4 - Prob. 50SYUCh. 4 - Prob. 51SYUCh. 4 - Prob. 52SYUCh. 4 - Prob. 53SYUCh. 4 - Prob. 54SYUCh. 4 - 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