A) Find the linearization of the function at the given point. f (r, y) = (x – y)² + 1, at (1,1). B) Find the volume of the solid bounded above by the cylinder y = r² and below by the region enclosed by the curves z = 2 –², z = x in the xz-plane

Q: (B) Integrate g(x,y,z)=x+y(x+2z) over the surface area of the region cut from plane x+2y+2z=5 by the…

A: What is Surface Integral: Surface integral is an iterated integration that is performed over a…

Q: Find the counterclockwise circulation of F = (y + ex ln y)i + (ex/y)j around the boundary of the…

A:

Q: An artist has decided to finish their piece of artwork by balancing it on a fulcrum and putting it…

A:

Q: Let R be the region bounded by y = 6.5 – x, the x axis and the y axis. 6 4 3 2 1 The solid obtained…

A:

Q: A fluid has density 1200 kg/m and flows with velocity = i + yj + zk, where x, y, and z are measured…

A:

Q: Find the flux F(x, y, z) = (xy²,x²y, ln(x + y)) directed outwards through the surface of the solid…

A:

Q: Let R be the region in the half plane x 2 0 bounded by the curves y = 3x-3 y = 1-x2 %3D x=0 Compute…

A:

Q: (a) Integrate g(x,y,z) = Inx+y over the surface of the region cut from the plane 4x+3y+2z=1 by the…

A:

Q: The region W lies between the spheres x2+y2+z2=1 and x2+y2+z2=9 and within the cone z=x2+y2−−−−−−√…

A: Given: The region W lies between the spheres       x2 + y2 + z2 = 1 and x2 + y2 + z2 =9 with in the…

Q: The solid region bounded on the sides by the paraboloid z = 4-x-y, above by the plane z= 3, and…

A: The Equation of paraboloid: z = 4-x2-y2The equation of upper plane: z = 3The equation of lower…

Q: Find the centroid (x, y) of the region bounded by the two curves y = sin x, y = 6 cos x, x = 0, and…

A:

Q: Integrate G(x, y, z)=x4 y ( y2 + z2 ) over the surface of the cylinder y2 +z2 = 25 that lies in the…

A:

Q: 3. Find the displacement u(r, t) in a vibrating circular elastic membrane of radius 1 that satisfies…

A:

Q: 4. Find the volume V of the solid S that is bounded by the elliptic paraboloid defined by 2x2 + y2…

A:

Q: A fluid has density 1000 kg/m3 and flows with velocity ū = xi + yj + zk, where x, y, and z are…

A: A fluid density 1000 kg/m3 andflows with velocity v→=xi→+yj→+zk→where x,y and z are measured…

Q: (b) A solid G is bounded above by x² + y² + z² – 4z – 12 = 0 and below by z = Vx² + y². Sketch the…

A:

Q: Find the sum of maximum and minimum values of the function f(x, y, z) = 9x + 18y + 27z on the elipse…

A: Using Lagrange Multipliers with Two Constraints to find the maximum and minimum values of the given…

Q: Find the x coordinate of the centroid of the solid formed in the first octant bounded above by…

A: Given the solid E is bounded by z=1-y2,x=1,x+y=3 in the first octant. Find the x coordinate of the…

Q: find Ix, Iy, I0, x, and y for the lamina bounded by the graphs of the equations. y = 0, y = 2, x =…

A: The value of I0,Ix,Iy.

Q: Let R be the region in the half plane x 2 0 bounded by the curves y=-5x + 5 y = x2 - 1 *= 0 Compute…

A: Solution

Q: 2). Find the flux of F(x, y, z) = (0, yz, z) outward through the surface S cut from the cylinder y +…

A:

Q: Find the coordinates of the centroid of the solid generated when the smaller region bounded by x² +…

A:

Q: (a) Find the center of mass of a semicircular plate of radius r. (b) Find the centroid of the region…

A: NOTE:- AS POSTED MULTIPLE INDEPENDENT QUESTIONS, WE ARE ANSWERING ONLY FIRST QUESTIONS AS PER…

Q: Find the volume of the solid bounded from above by the surface z = (64 − 4x^2 − 9y^2)^(1/3) and from…

A: To find - Find the volume of the solid bounded from above by the surface z = 64 - 4x2 - 9y213 and…

Q: Find the centroid (δ = 1) of the solid enclosed by the cylinder x2 + y2 = 4, bounded above by the…

A:

Q: y=1sin(πx)+5y=1sin(πx)+5 bounded by x = 0, x = 2, and y = 0 Draw the Lamina in an x-y plane and put…

A:

Q: 4. Find the volume of the solid under the surface f(x, y) = xy and above the triangular region in…

A: .

Q: Integrate R(x,y,z)=x (xy2 +z) over the surface of the cylinder x2 + y2 = 9 that lies between the…

A:

Q: Find the exact coordinates of the centroid for the region bounded by the curves 3x+2y=6, y=0, and…

A: to find the exact coordinates of centroid centroides are (x-,y-) x- =1area∫abxf(x)dx y-…

Q: Find the centroid of the solid generated if the region bounded by the y-axis, the lines y=1 and y =…

A:

Q: a) Integrate g(x,y,z) = Inx²+y over the surface of the region cut from the plane 4x+3y+2z=1 by the…

A:

Q: 3) Find the centroid of the plane region bounded by y = (x – 2)² and 2x – y = -4.

A:

Q: Integrate G(x, y, z) = x - y - z over the portion of the plane x + y = 1 in the first octant between…

A: Given G(x,y,z)=x-y-z

Q: 5. Evaluate [[ F • dS where F(x,y,z)= and S is the boundary of the solid region E enclosed by the…

A: Given: Evaluate  ∬S F. dS  Here, F(x, y, z) = <y, x, z> S is the boundary of the solid region…

Q: Find the coordinates of the centroid of the solid generated when the smaller region bounded by x² +…

A: Solution:   Given data, x2+y2-6ax=0x+y=6a we have to find centroid of solid formed by above equation…

Q: The volume of the solid generated by revolving the region between the parabola x =y²+1 and the line…

A:

Q: Integrate the function f(x, y, z) = (x2 + y2 + z2)4 over the part of the solid cone y2 + z2 ≤ x2…

A:

Q: a) Evaluate ||| x²yz dV, where G is solid in the first octant that is bounded by parabolic cylinder…

A:

Q: Integrate g(x, y, z) = x4y(y2 + z2 ) over the portion of the cylinder y2 + z2 = 25 that lies in the…

A:

Q: The solid in the first octant bounded by the coordinate planes and the plane z = 3 – x –y dz dy dx

A: Answer is:∫03∫03-x∫03-x-ydzdydx Proof is attached below.

Q: Let R be the region in the half plane x 20 bounded by the curves y = -5x + 5 y = x2 – 1 x = 0…

A:

Q: 5x²+2y²-3a²-z=0 and 2x² +5y²-4a² + z = 0 Determine the moment of inertia about the Oz-axis of the…

A: Given: The elliptical paraboloids are 5x2 + 2y2 - 3a2 - z = 0 and 2x2 + 5y2 - 4a2 + z = 0. To find:…

Q: (a) Integrate g(x,y,z) = Inx²+y over the surface of the region cut from the plane 4x+3y+2z=1 by the…

A:

Q: b) Use the Gauss-divergence Theorem to find the surface integral ff, F.n ds, where S is cylinder x²…

A: As stated in question we will use Gauss-divergence Theorem to solve this question.

Q: (a) Integrate g(x,y,z) = lnx'+y over the surface of the region cut from the plane 4x+3y+2z=1 by the…

A: Please comment if you need any clarification. If you find my answer useful please put thumbs up.…

Q: find the outward flux of F across the boundary of D. F = (6x + y)i - (x + z)j + 4yz k D: The region…

A:

Q: integrate the given function over the given surface. H(x, y, z) = x2√(5 - 4z), over the…

A: Application of integration: We can use cylindrical coordinate to find a parametric equation for the…

Q: Find the value of a if the centroid of the region bounded by the parabola y² = 4px and the line = a…

A:

Q: Find the absolute maximum and minimum Of the function f(x, y) = x + Y on the elliptic region {(x, y)…

A: