Deck 13: Extension H: Vector Calculus

Question 1

Evaluate the surface integral. S is the part of the plane that lies in the first octant.

A)
B)
C)
D)
E)

Answer 1

Question 2

Evaluate the surface integral for the given vector field F and the oriented surface S.In other words,find the flux of F across S.

Answer 2

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Question 3

Evaluate the surface integral.Round your answer to four decimal places. S is surface

A)
B)
C)
D)
E)

Answer 3

Question 4

Find the moment of inertia about the z-axis of a thin funnel in the shape of a cone if its density function is

Question 5

Use Gauss's Law to find the charge contained in the solid hemisphere ,if the electric field is

Question 6

Evaluate the surface integral for the given vector field F and the oriented surface S.In other words,find the flux of F across S. in the first octant,with orientation toward the origin.

Question 7

Suppose that where g is a function of one variable such that Evaluate where S is the sphere

A)
B)
C)
D)
E) None of these

Question 8

The temperature at the point in a substance with conductivity is Find the rate of heat flow inward across the cylindrical

A)
B)
C)
D)
E)

Question 9

A fluid with density flows with velocity Find the rate of flow upward through the paraboloid