4. Obtain the equation of the tangent plane to the surface with parametric representation r(u, v) = u²i + 2u sin vj + u cos v k %3D at (1,0, 1).
4. Obtain the equation of the tangent plane to the surface with parametric representation r(u, v) = u²i + 2u sin vj + u cos v k %3D at (1,0, 1).
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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Please need solution for number 4;5 and 6
![4. Obtain the equation of the tangent plane to the surface with parametric
representation
r(u, v) = u²i + 2u sin v j + u cos v k
at (1,0,1).
5. Calculate the area of the part of the plane
x = y? + z?
that lies inside the cylinder y? + z? = 9.
6. Determine the area of the surface with vector equation
r(u, v) = (u – v,3+ 2u, 1 – u + v)
that is given by 0 <u< 2,–2 < v < 3.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa72ef3a7-0745-4034-8c72-4316fdb0ff7b%2Fc3f193d1-fa37-441e-9de9-18c14262a5c9%2Fej26jyq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:4. Obtain the equation of the tangent plane to the surface with parametric
representation
r(u, v) = u²i + 2u sin v j + u cos v k
at (1,0,1).
5. Calculate the area of the part of the plane
x = y? + z?
that lies inside the cylinder y? + z? = 9.
6. Determine the area of the surface with vector equation
r(u, v) = (u – v,3+ 2u, 1 – u + v)
that is given by 0 <u< 2,–2 < v < 3.
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