Calculas 3 Surface Integral 2 problems Give a parametric description of the form r(u,v) = (x(u,v),y(u,v),z(u,v)) for the frustum of the cone z =x +y, for 3 sz 6.Select the correct choice below.O A. r(u,v) = (6v cos u,3v sin u,v), 0sus 2T, 3svs6O B. r(u,v)= (v cos u,v sin u,v), 0sus2r, 3svs6O C. r(u,v) = (6v cos u,3v sin u,v), 0sus 2r, 3svs6O D. r(u,v)=C u,2sin u,v), 0su 2n, 3 Give a parametric description of the form r(u,v) = (x(u,v),y(u,v),z(u,v)) for the following surface.The cap of the sphere x + y+z = 49, for2Select the correct choice below and fill in the answer boxes to complete your choice.(Type any angle measures in radians. Use angle measures greater than or equal to 0 and less than 2n. Type exact answers in termsO A. r(u,v)= (7 cos u sin v,7 sin u sin v,7 sin v) forandB. r(u,v) = (7 cos u,7 sin u,v) for

Since you have asked multiple questions, we will solve the first question for you. If you want any specific question to be solved then please specify the question number or post only that question. In cylindrical coordinates, x=r cosθ, y=r sinθ, z=z. Change to u-v plane. x=v cos u, y=v sinu, z=z. From the equation of the cone z2=x2+y2, z2=(v cosu)2+(v sinu)2 =v2 cos2u+v2 sin2u =v2 gives z=v.Since 3≤z≤6, 3≤v≤6 and 0≤u≤2π. Thus the parametric description for the given frustum of cone is r(u,v)=v cos u, v sin u, v, 0≤u≤2π, 3≤v≤6. Option B is correct.

Math

Advanced Math

Give a parametric description of the form r(u,v) = (x(u,v),y(u,v),z(u,v)) for the frustum of the cone z = x +y, for 3szs6. Select the correct choice below. A. r(u,v) = (6v cos u,3v sin u,v), 0sus 2n, 3 svs6 O B. r(u,v) = (v cos u,v sin u,v), 0sus2n, 3 svs6 OC. r(u,v) = (6v cos u,3v sin u,v), 0sus2n, 3svs6 O D. r(u,v)= sin u,v), 0 sus 2n, 3svs6 cosu, O E. r(u,v) = (2v cos u,2v sin u,v), 0sus2n, 3svs6

Give a parametric description of the form r(u,v) = (x(u,v),y(u,v),z(u,v)) for the frustum of the cone z = x +y, for 3szs6. Select the correct choice below. A. r(u,v) = (6v cos u,3v sin u,v), 0sus 2n, 3 svs6 O B. r(u,v) = (v cos u,v sin u,v), 0sus2n, 3 svs6 OC. r(u,v) = (6v cos u,3v sin u,v), 0sus2n, 3svs6 O D. r(u,v)= sin u,v), 0 sus 2n, 3svs6 cosu, O E. r(u,v) = (2v cos u,2v sin u,v), 0sus2n, 3svs6

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

Calculas 3 Surface Integral 2 problems

Give a parametric description of the form r(u,v) = (x(u,v),y(u,v),z(u,v)) for the frustum of the cone z =x +y, for 3 sz 6.
Select the correct choice below.
O A. r(u,v) = (6v cos u,3v sin u,v), 0sus 2T, 3svs6
O B. r(u,v)= (v cos u,v sin u,v), 0sus2r, 3svs6
O C. r(u,v) = (6v cos u,3v sin u,v), 0sus 2r, 3svs6
O D. r(u,v)=
C u,
2
sin u,v), 0su 2n, 3<vs6
E. r(u,v)= (2v cos u 2v sin u,v), 0su<2x, 3<v<6

Give a parametric description of the form r(u,v) = (x(u,v),y(u,v),z(u,v)) for the following surface.
The cap of the sphere x + y+z = 49, for
2
Select the correct choice below and fill in the answer boxes to complete your choice.
(Type any angle measures in radians. Use angle measures greater than or equal to 0 and less than 2n. Type exact answers in terms
O A. r(u,v)= (7 cos u sin v,7 sin u sin v,7 sin v) for
and
B. r(u,v) = (7 cos u,7 sin u,v) for
<us
and
C. r(u v)= (7 sin u cos v,7 sin u sin v,7 cos u) for
and
D. r(u.v)= (49 cos u,49 sin u,v) for
<us
and
es

With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.

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