The tangent plane at a point Po (f(uovo) 9 (uo.vo),h(uo.vo)) on a parametrized surface r(u,v) = f(u, v) i + g(u,v) j+h(u,v) k is the plane through Po normal to the vector ru (uovo) xrv (uovo), the cross product of the tangent vectors ru (40,vo) and rv (uo.vo) at Po. Find an equation for the plane tangent to the surface at Po. Then find a Cartesian equation for the surface and sketch the surface and tangent plane together. The circular cylinder r(0,z) = (3 sin (20))i + (6 sin²0) j+z k at the point Po 3√3 9 2 ¹2 1 -₁)₁ -1 corresponding to (0,z) = - (5-1) An equation for the plane tangent to the surface at Po is (Type an equation using x, y, and z as the variables.)
The tangent plane at a point Po (f(uovo) 9 (uo.vo),h(uo.vo)) on a parametrized surface r(u,v) = f(u, v) i + g(u,v) j+h(u,v) k is the plane through Po normal to the vector ru (uovo) xrv (uovo), the cross product of the tangent vectors ru (40,vo) and rv (uo.vo) at Po. Find an equation for the plane tangent to the surface at Po. Then find a Cartesian equation for the surface and sketch the surface and tangent plane together. The circular cylinder r(0,z) = (3 sin (20))i + (6 sin²0) j+z k at the point Po 3√3 9 2 ¹2 1 -₁)₁ -1 corresponding to (0,z) = - (5-1) An equation for the plane tangent to the surface at Po is (Type an equation using x, y, and z as the variables.)
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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Question
2. A cartesian equation for the surface is?
3. Draw the graph and the tangent plane
Transcribed Image Text:The tangent plane at a point Po (f(uovo) 9 (uo.vo),h(uo.vo)) on a
parametrized surface r(u,v) = f(u, v) i + g(u,v) j+h(u,v) k is the plane through
Po normal to the vector ru (uovo) xrv (uovo), the cross product of the
tangent vectors ru (40,vo) and rv (uo.vo) at Po. Find an equation for the
plane tangent to the surface at Po. Then find a Cartesian equation for the
surface and sketch the surface and tangent plane together.
The circular cylinder r(0,z) = (3 sin (20))i + (6 sin²0) j+z k at the point
Po
3√3 9
2 ¹2
1
-₁)₁
-1 corresponding to (0,z) =
- (5-1)
An equation for the plane tangent to the surface at Po is
(Type an equation using x, y, and z as the variables.)
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