Exam 15: Section 6: Vector Analysis

Evaluate , where .

Evaluate , where S is , first octant.

Find the flux of through S, , where is the upward unit normal vector to S.

Evaluate , where and S is given by .

Evaluate , where .

Evaluate , where .

Let S be the surface oriented upwards. Use a computer algebra system to find the rate of mass flow of a fluid of density through S if the velocity field is given by .

Let be an electrostatic field. Use Gauss's Law to find the total charge enclosed by the closed surface consisting of the hemisphere and its circular base in the xy-plane.

Use a computer algebra system to evaluate where S is . Round your answer to two decimal places.

Find the flux of over the closed surface (let be the outward unit normal vector of the surface). S: cube bounded by

Find the flux of through where N is the upward unit normal vector to S.

Evaluate , where and S is given by .

Evaluate , where and S is given by .

Use a computer algebra system to evaluate where S is . Round your answer to two decimal places.

Find the flux of through S, , where is the upward unit normal vector to S. , first octant

Find the mass of the surface lamina S of density .

Find for the lamina with uniform density of 1. Use a computer algebra system to verify your result.

Evaluate , where .