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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
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.
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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