(a) Use Stokes' theorem to evaluate as viewed from above. F. dr = ²/F₁ F. dr, where F(x, y, z) = x²yi + i+\/x³j+ + xyk and C is the curve of intersection of the hyperbolic paraboloid z = y² - x² and the cylinder x² + y² = 1, oriented counterclockwi (b) Use a computer to graph both the hyperbolic paraboloid and the cylinder with domains chosen so that you can see the curve C and the surface that you used in part (a). Find parametric equations for C and use them to graph C. (Select Update Graph to see your response plotted on the screen. Select the Submit button to grade your response.) (x(t), y(t), z(t)) = for 0 st s 2 Update Graph Student Response Response Description
(a) Use Stokes' theorem to evaluate as viewed from above. F. dr = ²/F₁ F. dr, where F(x, y, z) = x²yi + i+\/x³j+ + xyk and C is the curve of intersection of the hyperbolic paraboloid z = y² - x² and the cylinder x² + y² = 1, oriented counterclockwi (b) Use a computer to graph both the hyperbolic paraboloid and the cylinder with domains chosen so that you can see the curve C and the surface that you used in part (a). Find parametric equations for C and use them to graph C. (Select Update Graph to see your response plotted on the screen. Select the Submit button to grade your response.) (x(t), y(t), z(t)) = for 0 st s 2 Update Graph Student Response Response Description
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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Transcribed Image Text:(a) Use Stokes' theorem to evaluate
as viewed from above.
S
F. dr =
/² F · dr, where F(x, y, z) = x²yi + ½x³j+ + xy k and C is the curve of intersection of the hyperbolic paraboloid z = y² - x² and the cylinder x² + y² = 1, oriented counterclockwise
(b) Use a computer to graph both the hyperbolic paraboloid and the cylinder with domains chosen so that you can see the curve C and the surface that you used in part (a).
Find parametric equations for C and use them to graph C. (Select Update Graph to see your response plotted on the screen. Select the Submit button to grade your response.)
(x(t), y(t), z(t)) =
Update
Graph
Student Response
2
Z
for 0 ≤ t ≤ 2π
2
Response
Description
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