Changing the order of integration Rewrite the following integrals using the indicated order of integration and then evaluate the resulting integral. 39. ∫ 0 5 ∫ − 1 0 ∫ 0 4 x + 4 d y d x d z in the order dz dx dy
Changing the order of integration Rewrite the following integrals using the indicated order of integration and then evaluate the resulting integral. 39. ∫ 0 5 ∫ − 1 0 ∫ 0 4 x + 4 d y d x d z in the order dz dx dy
Changing the order of integrationRewrite the following integrals using the indicated order of integration and then evaluate the resulting integral.
39.
∫
0
5
∫
−
1
0
∫
0
4
x
+
4
d
y
d
x
d
z
in the order dz dx dy
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
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.
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.
Chapter 16 Solutions
Calculus: Early Transcendentals, Books A La Carte Edition (3rd Edition)
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