Calculate ff A.n ds If A = yi + 2xj – zk and S is a 2x + y = 6 plane surface in the first octane cut by the z = 4 plane.

Q: If (a,ß.r) is a point at which the surface x2+y2-z-2x+42=0 has a horizontal tangent plane, then Iyl=

A: Horizontal tangent plane

Q: Find ervstion for the tangen plare to the Surface an Siven by x2y?3 =12 at the point Z-2,1,3)

A:

Q: Evaluate ff.dS, where (a) v = (xy, -x², x +z) and S is the part of the plane 2x + 2y + z = 6…

A: Problem is solved using concept of double integral.

Q: Evaluate the surface SS₂ xz ds S is the part of the 2x+2y+z=4 that li- the first octant.

A:

Q: Calculate , z² dS if S is the prism whose base is the triangle in the limited xy plane by the x axis…

A: Here given figure is Since prism has 5 surfaces (1)-OAB (2) OADE (3) CDE (4) OBCD (5) ABCE

Q: Find the surface area of the part of the paraboloid z = 9 – 2.x - 2y that lies above the %3D

A:

Q: (a) Prove that M: (x² + y^y° + 3z² = 1 is a surface. (b) For which values of e is M: z(z – 2) + xy =…

A: Consider the provided question, (a)

Q: Evaluate f, A.n ds, where A = zi +j- 3y²zk and S is the surface of cylinder x? + y? = 16 included in…

A:

Q: Classify the surface: 1-z = 3y? + 4z? ,2

A: Given : The surface 1 - x = 3y2 + 4z2   To classify the given surface.

Q: 25. Evaluate F.N dS where F= yl + 2xj –- zk and S is the surface of the plane 2x +ye 6 in the first…

A:

Q: Identify a generating curve on the XZ-plane for the surface of revolution with equation x? + y? + Z?…

A: We need to identify a generating curve on the xz-plane for the surface of the revolution with the…

Q: 8. Let S be the surface {(x, y, 2) | a = y? + 22 + 1}. Find every point (ro, yo, zo) on S so that…

A:

Q: Evaluate ſ F . n dS if F = (x + y² ™)ī − (2x)j + (2yz)k and $ is the surface of the plane 2x + y +…

A:

Q: If A = 18zî – 12j + 3yk then find SS,A.ñds where S is the surface of the plane %3D 2x + 3y + 6z = 12…

A: Given, surface S: 2x+3y+6z=12           and                       A→=18zi^-12j^+3yk^

Q: (3) Consider the quadric surface SC R, having equation a2 + y? – 22 = 9. Find all lines through P =…

A: The quadratic equation is given by x2+y2-z2=9.  General equation of line is: x,y,z=a,b,c+tl,m,n…

Q: The value of . (x² +y²) dS, where S is the surface of the paraboloid z = 2- (x² + y2 ) above the x-y…

A:

Q: sketch the given surface. x2 − 4y2 = z

A: Given: x2-4y2=z Divide the equation both sides by 4. x24-4y24=z4x222-y21=z4 The equation…

Q: 1. Find the area of the surface the part of the plane 3x + 2y + z = 6 that lies on the first octant

A:

Q: Find the surface area of the plane ( 15x- 5z+20y=35) if it is in the first octant

A: Solution:-

Q: ? Find the surface area of the plane ( 15x-5z+20y%3D35) if it is in the first octant

A: Here we have to find the surface area of the plane 15x-5z+20y=35 ................... (1) for the…

Q: Classify the surface: 1 – x = 3y + 4z?

A: Given :  The surface 1 - x = 3y2 + 4z2.   To classify the given surface.

Q: 2. Find the area of the part of the sphere x² + y² + z² = 4z that lies inside the paraboloid z = x²…

A:

Q: Find the area of the part of the paraboloid z=x +y² that lies under the plane 2=9.

A:

Q: ✓ Evaluate s SS₁ (Oxu). A, where A = 347-127 +92R Z=2 and S is the surface of paraboloid 22 = x=79²…

A:

Q: Find the points on the surface z2 = xy + 4 closest to the origin.

A:

Q: Identify a generating curve on the XZ-plane for the surface of revolution with equation x? + y2 + z?…

A: Given: Surface of revolution with the equation x2+y2+z2=e2x To find: Identify a generating curve on…

Q: Sketch the surface z = 3x? + y? +1 and find its linear approximation at P-(0, -1)

A:

Q: Find vohume fome above ZVy-xLy, below Z0(xy plane) inside xy/ 3.

A:

Q: Let W be the region that is cut out from r² + y² < 4 by the paraboloid z = r² + y² and the plane z =…

A:

Q: Find the area of the part of the paraboloid z=x² + y² that lies under the plane z=9.

A:

Q: Find a generating curve and the axis of revolution for the surface                             x2 +…

A: Find a generating curve and the axis of revolution for the surface   x2+3y2+z2 =9 If the equation of…

Q: sketch the given surface. x2 + y2 − z 2= 1

A: Given: x2 + y2 − z 2= 1

Q: Find the surface area of the portion of the part of the paraboloid z = 3 – x² – y² that lies above…

A: Given z = 3-x2-y2 , above the plane z=-1

Q: Find the area of the cap cut from the paraboloid y2 + z2 = 3x by the plane x = 1.

A:

Q: 7. Use a program to plot the surface generated by the following equation: 4x – 16y + z? = 16

A: we need to plot the following surface generated by, 4x2-16y2+z2=16

Q: a) Evaluate ff, (2x – z) dS, where S is part of the plane 3x + 2y + z = 1 that lies above the…

A: Surface integral

Q: Find a generating curve on the xz-plane for the surface of revolution with equation x2+ y²+ z²= e2x…

A: The solution is given below

Q: If A = 18zî – 12ĵ + 3yk then find Jſ, A.ñ ds where S is the surface of the plane %3D 2x + 3y + 6z =…

A: Note "As per our company guidelines we are supposed to answer ?️only first question. Kindly repost…

Q: 7. Consider the Surface S:z = 52² + 5y?. An equation of the plane tangent to Sat the point P (3, 3,…

A:

Q: Verify that the line r(t) = [1 + t, 1 - t, t] is part of the one sheeted hyperboloid x^2 + y^2 -…

A:

Q: Given that o is the part of the surface z = 4 – x in

A: Given, the surface z = 4 - x in the first octant from y = 0  to  y = 2. If ψx, y, z=xyz, F(x, y, z)…

Q: Find the points on the surface z =xy+36 that are closest to the origin. O a. (0, 0, 6) b. (0, 0, 36)…

A:

Q: Compute 5xy ds, where S is the surface of the tetrahedron with sides z = 0, y = 0, x + z = 1, and x…

A:

Q: Evaluate Sſ Ands where A= (x+y*)î – 4xj +4yzk and s is the surface of the plane, 2x+y+2z=8 in the…

A:

Q: Find any points on the hyperboloid  x2 − y2 − z2 = 6  where the tangent plane is parallel to the…

A:

Q: Find the area of the surface of the part of the plane 3x + 2y + 4z = 2 that lies inside the cylinder…

A: Here, surface S has an equation of the form z=f(x,y), where (x,y)  D and f has continuous partial…

Q: (a) Find the surface area of the plane 3x +2y + z = 6 that lies in the first octant.

A: If z=fx, y then surface area is, AS=∫∫D1+zx2+zy2dA

Q: Evaluate F. dS, where F = 6xy²i + 6x²yj + 2z°k and S is the surface of the unit sphere.

A: