Answered: 40.x = u', y = v², z = uv; u = 1, v = 1

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40.x = u', y = v², z = uv; u = 1, v = 1

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section: Chapter Questions

Problem 17T

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Question

40) Find an equation of the tangent plane to the parametric surface at the given point. If you have software that graphs parametric surfaces, use a computer to graph the surface and the tangent plane. x = u^2, y = v^2, z = uv; u = 1, v = 1

39-43 Find an equation of the tangent plane to the parametric sur-
face at the given point. If you have software that graphs parametric
surfaces, use a computer to graph the surface and the tangent plane.
39. x = u + v, y = 3u², z = u v;
—
(2,3,0)
40.x=u², y=v², z = uv; u = 1, v = 1
41. r(u, v) = u² i + 2u sin v j + u cos vk; u = 1, v = 0
42. r(u, v)
=
uvi + u sin vj + v cos u k; u = 0, v = π
43. r(u, v) = ui + ln(uv) j + vk; u = 1, v = 1

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