Exam 15: Section 5: Vector Analysis

Find the rectangular equation for the surface by eliminating the parameters from the vector-valued function and sketch the graph.

The surface of the dome on a new museum is given by and is in meters. Find the surface area of the dome.

Find a vector-valued function whose graph is the part of the paraboloid that lies inside the cylinder .

Find the area of the surface given by , where .

Determine the tangent plane for the hyperboloid .

Find an equation of the tangent plane to the surface represented by the vector-valued function at the given point.

Find a vector-valued function whose graph is the ellipsoid .

Find a vector-valued function whose graph is the cylinder .

Find a vector-valued function whose graph is the cone .

Identify the surface by eliminating the parameters from the vector-valued function .

Write a set of parametric equations for the surface of revolution obtained by revolving the graph of the function about the x-axis.

Find the area of the surface over the given region. Use a computer algebra system to verify your results. The part of the cone, where .

Find the rectangular equation for the surface by eliminating parameters from the vector-valued function. Identify the surface.

Match the following vector-valued function with its graph.

Match the following vector-valued function with its graph.

Find a vector-valued function for the hyperboloid .

Find a vector-valued function whose graph is the plane .

Find the area of the surface of revolution .

Find the rectangular equation for the surface by eliminating the parameters from the vector-valued function .

Write a set of parametric equations for the surface of revolution obtained by revolving the graph of the function about the given axis.