Verify Formula (1) in the Divergence Theorem by evaluating the surface integral and the triple integral. F x , y , z = x y + y z j + x z k ; σ is the surface of the cube bounded by the planes x = 0 , x = 2 , y = 0 , y = 2 , z = 0 , z = 2.
Verify Formula (1) in the Divergence Theorem by evaluating the surface integral and the triple integral. F x , y , z = x y + y z j + x z k ; σ is the surface of the cube bounded by the planes x = 0 , x = 2 , y = 0 , y = 2 , z = 0 , z = 2.
Verify Formula (1) in the Divergence Theorem by evaluating the surface integral and the triple integral.
F
x
,
y
,
z
=
x
y
+
y
z
j
+
x
z
k
;
σ
is the surface of the cube bounded by the planes
x
=
0
,
x
=
2
,
y
=
0
,
y
=
2
,
z
=
0
,
z
=
2.
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.
Evaluate the circulation of G = xyi + zj + 4yk around a square of side 4, centered at the
origin, lying in the yz-plane, and oriented counterclockwise when viewed from the positive x-axis.
Circulation =
Jo
F. dr
=
Find a parametrization of the surface z = 3x² + 8xy and use it to find the tangent plane at x = 1, y = 0, z = 3.
(Use symbolic notation and fractions where needed.)
z =
Evaluate the circulation of G = xyi+zj+7yk around a square of side 9, centered at the origin, lying in the yz-plane, and oriented counterclockwise when viewed from the positive
x-axis.
Circulation =
Prevs
So F.dr-
Chapter 15 Solutions
Calculus Early Transcendentals, Binder Ready Version
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