Exam 13: Extension H: Vector Calculus

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

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

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.

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

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.

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

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

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

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