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3. 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(2), 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?

3. 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(2), 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?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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3. 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)?
Transcribed Image Text:3. 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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