Compute the surface integral s F-ndo. F = xyi - x¹j+ (x+z)k. The surface is the top of the plane 2x + 2y +z = 6 included in the first octant.

Q: 7y² Consider the quadric surface r² + the usual coordinate axes, i.e. so that the principal axes are…

A:

Q: Verify Stokes' theorem where A = (x-z)i + (x³ +zy)j - 3x y²k and S is the surface of z=2-√√x² + y²…

A:

Q: Consider the surface z = (x + 1)² + (y – 2)² – 1 - Select an equation of the tangent plane to the…

A: we have to find the equation of the tangent plane of the surface 2=(x+1)2+(y-2)2-1 atthe point…

Q: A surface in R³ is defined by the equation 4z = x² + 4y“.

A:

Q: Is the set {(x, y, z) = R³; z = 0 and x² + y² ≤ 1} a regular surface? Is the set {(x, y, z) = R³; z…

A: Solution:-  (a) This is not a regular surface because a neighborhood of a boundary point like (1, 0,…

Q: The points on the surface x2−2y2−3z2 = 33 at which the tangent plane is parallel to the 8x+4y+6z=5…

A:

Q: Find the area of the surface. The part of the plane z = 5 + 5x + 2y that lies above the rectangle…

A: given  z = 5 + 5x + 2y               ⇒  ∂z∂x = 5   and  ∂z∂y = 2                  ds =…

Q: i-2yj + (z+3)k and suppose the outward flux of F through Side A is 1 and through Side B is -3. Can…

A: answer is in next step

Q: Let C be the positively oriented square with vertices (0, 0), (3, 0), (3, 3), (0, 3). Use Theorem to…

A:

Q: Evaluate F.ndS for the given F and o. (b) F(x, y, z) = (x² + y) i+ xyj– (2xz + y) k, o: the surface…

A:

Q: Suppose f : R+ R is continuous and f(0) = 0. Consider the limit yf(x) lim (x,y) (0,0) y² + f (x)2*…

A:

Q: Prove that the z-axis is a nodal line with unodes a -2) and (0, 0,2/3) for the surface 3 2xy +…

A:

Q: Verify Stoke's theorem for A=(2x-y)i-yz²j-y*zk where S is the upper half 5A. surface of the sphere *…

A: Consider the given vector and sphere equation. A→=2x−yi−yz2j−y2zk and x2+y2+z2=1 Since S is the…

Q: Apply Gauss's theorem to evaluate. A

A:

Q: Let C be an ellipse in a horizonal plane lying above the xy-plane. Which type of quadric surface is…

A: Given, Let C be an ellipse in a horizontal plane lying above the xy-plane.

Q: Find the traces of the given surface in the planes x = k, y = k, z = k. Then identify the surface…

A: Given the surfaces, we need to find the traces on the planes x=k,y=k,z=k.(a)Consider the surface…

Q: Exercise 5. Compute F F.NdS where F(x, y, z) surface of the plane x + 2y + z = 6 in the first…

A:

Q: b) Use Gauss' theorem to evaluate RR F. ndS where F = (x² - y)i + y³z²j + (xy – y²z³)k UTM UTM and o…

A:

Q: Locate and classify the stationary points on the surface z=xy2-2xy-2x2-3x, remembering that  x, y ,…

A: Solving for stationary points of given function using partial derivatives

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: Consider the surface x² - y² + z² = −4. A. Identify the name of the surface. B. The line…

A: We know general form of hyperboloid of two sheets is  -x2a2-y2b2+z2c2=1 where positive term is the…