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Let S be the quadratic surface given by S = {(x, y, z) | z = 4x² - y², z ≥ 0}, oriented with the upward pointing normal and parameterized by Þ(u, v) = (u, v, 4 – u² – ²). Let F= yzi-xzj+k. Give the associated tangent vectors Tu and T, and the normal vector Tu x Tv. Give your answers in the form (*, *, * ). Tu(u, v) = Ty(u, v) = Tux Tv (u, v) = Calculate the value of the surface integral I = -2 T 0 -4 T 2π ¹ = // ₂₁ S 4 T F. ds.

Let S be the quadratic surface given by S = {(x, y, z) | z = 4x² - y², z ≥ 0}, oriented with the upward pointing normal and parameterized by Þ(u, v) = (u, v, 4 – u² – ²). Let F= yzi-xzj+k. Give the associated tangent vectors Tu and T, and the normal vector Tu x Tv. Give your answers in the form (*, *, * ). Tu(u, v) = Ty(u, v) = Tux Tv (u, v) = Calculate the value of the surface integral I = -2 T 0 -4 T 2π ¹ = // ₂₁ S 4 T F. ds.

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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Let S be the quadratic surface given by S = {(x, y, z) | z = 4 - x² - y², z ≥ 0}, oriented with the upward pointing normal and parameterized by Þ(u, v) = (u, v, 4 − u² v²). Let F= yzi-xzj+k. Give the associated tangent vectors T, and T, and the normal vector T₂ × Tv. Give your answers in the form (*, *, * ). Tu(u, v) = T, (u, v) = Tu x Tv (u, v) = Calculate the value of the surface integral I = O -2π -4 T 2π •//. F 4 π F. ds.
Transcribed Image Text:Let S be the quadratic surface given by S = {(x, y, z) | z = 4 - x² - y², z ≥ 0}, oriented with the upward pointing normal and parameterized by Þ(u, v) = (u, v, 4 − u² v²). Let F= yzi-xzj+k. Give the associated tangent vectors T, and T, and the normal vector T₂ × Tv. Give your answers in the form (*, *, * ). Tu(u, v) = T, (u, v) = Tu x Tv (u, v) = Calculate the value of the surface integral I = O -2π -4 T 2π •//. F 4 π F. ds.
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