. Recall that the surfaces x + y = sin (z) and x + y = (ln(z)) are called…

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. Recall that the surfaces x² + y² = sin² (z) and x² + y² = (ln(z))² are called surfaces of

revolution (Because they can be generated by rotating sin(t) or ln(t) about the z-axis).

With that in mind, consider the surface S defined by

|x + y = sin(z) + 1

(a) What is the difference between the surface S and the surface |x|+|y| = sin(z), both

in the equation itself and the graph?

(b) Fix a value for z. What does the graph of the resulting equation look like?

(c) Fix a value for z. What is the area of the resulting shape?

(d) Obviously this is not a surface of revolution. How would you describe the class of

surfaces defined by |x| + y = f(z)?

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