Families of Surfaces in Cylindrical Coordinates

The graph of the equation in cylindrical coordinates


is shown below. Vary the parameters a, b, and c and observe the effect on the surface.

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Exercises

3. Describe the effect that changing the value of a has on the graph.

4. What role does the value of b play in the shape of the surface for integer values? Then describe the effect that changing the value of b has on the graph for non-integer values.

5. Describe the effect that changing the value of c has on the graph.
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