The tangent plane at a point Po (f(uo.vo).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 (uo.Vo) xrv (uo.vo), the cross product of the tangent vectors ru (uo.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) = (4 sin (20))i + (8 sin²0) j+z k at the point Po (2√3,6,-1) corresponding to A (0,z) = An equation for the plane tangent to the surface at Po is (Type an equation using x, y, and z as the variables.) A Cartesian equation for the surface is (Type an equation using x, y, and z as the variables.) Choose the correct graph of the surface, point, and tangent plane below. O A. y OB. OC.
The tangent plane at a point Po (f(uo.vo).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 (uo.Vo) xrv (uo.vo), the cross product of the tangent vectors ru (uo.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) = (4 sin (20))i + (8 sin²0) j+z k at the point Po (2√3,6,-1) corresponding to A (0,z) = An equation for the plane tangent to the surface at Po is (Type an equation using x, y, and z as the variables.) A Cartesian equation for the surface is (Type an equation using x, y, and z as the variables.) Choose the correct graph of the surface, point, and tangent plane below. O A. y OB. OC.
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:The tangent plane at a point Po (f(uo.vo) 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 (uo.vo) xrv (uo.vo), the cross
product of the tangent vectors ru (uo.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) = (4 sin (20))i + (8 sin²0) j+z k at the point Po (2√3,6,-1) corresponding to
t
(0,z) =
An equation for the plane tangent to the surface at Po is
(Type an equation using x, y, and z as the variables.)
A Cartesian equation for the surface is
(Type an equation using x, y, and z as the variables.)
Choose the correct graph of the surface, point, and tangent plane below.
O A.
y
OB.
O C..
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