Exam 15: Section 8: Vector Analysis

Let and let S be the plane in the first octant. Verify Stokes's Theorem by evaluating as a line integral and as a double integral.

Use Stokes's Theorem to evaluate where and S is the first-octant portion of over Use a computer algebra system to verify your result.

Use Stokes's Theorem to evaluate where and S is .Use a computer algebra system to verify your result.

Use Stokes's Theorem to evaluate .Use a computer algebra system to verify your results. Note: C is oriented counterclockwise as viewed from above.

Use Stokes's Theorem to evaluate where and S is over in the first octant. Use a computer algebra system to verify your result.

Find the curl of the vector field

Use Stokes's Theorem to evaluate where and S is the first-octant portion of over . Use a computer algebra system to verify your result.

Let and let S be the graph of . Verify Stokes's Theorem by evaluating as a line integral and as a double integral.

The motion of a liquid in a cylindrical container of radius 1 is described by the velocity field Find where S is the upper surface of the cylindrical container.

Find the curl of the vector field

Find the curl of the vector field

Find the curl of the vector field .

The motion of a liquid in a cylindrical container of radius 1 is described by the velocity field Find where S is the upper surface of the cylindrical container.

Use Stokes's Theorem to evaluate Use a computer algebra system to verify your results. Note: C is oriented counterclockwise as viewed from above. C: triangle with vertices

Verify Stokes's Theorem by evaluating as a line integral and as a double integral .

Let and let S be the graph of oriented counterclockwise. Use Stokes's Theorem to evaluate .

Use Stokes's Theorem to evaluate Use a computer algebra system to verify your results. Note: C is oriented counterclockwise as viewed from above.