Obtain the Solution x, y > 0, xy > 1 of the PDE 2y on the x+y 1 Uxy such that u = x+y 0, ux hyperbola ry =1.

Q: Compute the triple integral and please show work

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Q: xxS y dS S is the part of the paraboloid y= x 2 + z2 that lies inside the cylinder x 2 + z2 =4

A: And the projection of S onto the xz-plane is given by the disk So using the parameterization in x…

Q: 1 The domain of the function f(x,y)= + In(4- 4x2 - y?) is the region inside the x²+4y² – 4 ellipse…

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Q: Integrate H(x, y, z) = x2sqrt(5 - 4z), over the parabolic dome z = 1 - x2 - y2, z>=0.

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Q: Transform the equation rydx – (z+2) dy = 0 into the form of a %3D variable separable f(z) dz + g(y)…

A: Here, the given differntial equation is: xy dx-(x+2)dy=0...(1) To write the eqaution in form of f(x)…

Q: 8.Evaluate the triple Integral. Te by The paraboloid X=2yt + 2z? and the plane X=2. 7x dV, where E…

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Q: Find a parametrization for the cylinder x^2 + y^2 = 4.

A: Given: x2+y2=4

Q: 7. Derive the orthogonal trajectories of the family of hyperbolas xy = c. %3D

A: The solution are next step

Q: evaluate both the line integral and the double integral. 16. P(x, y) = 2x – x³y°, Q(x, y) = x³y°, C…

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Q: Evaluate the line integral x +1 ds /1+4x² Vĩ where C is the part of the parabola y = 9 – x² from…

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Q: Find a parametrization of the cylinder x2 + ( y - 3)2 = 9, 0 ≤z ≤ 5.

A: Given, the cylinder                         We have to find a parameterization of this given…

Q: Find the extreme values of ƒ(x, y, z) = x( y + z) on the curve of intersection of the right circular…

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Q: Find the sum of maximum and minimum values of the function f(x, y, z) = 4x + 8y + 12z on the elipse…

A: Lagrange's multiplier method uses the system of the equations obtained from the partial derivatives.…

Q: The plane x+ y = 1 intersects the paraboloid z = in a parabola. Parametrize the whole parabola using…

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Q: Find the minimum of f(x,y) = 8x + 2y on the ellipsoid 9x² + 3y² = 2. Leave your answer correct to…

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Q: Find the minimum of f(x,y) = 5x + 4y on the ellipsoid 6x2 + 4y2 = 3. Leave your answer correct to t…

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Q: Find the minimum of f(x,y) = 3x + 3y on the ellipsoid 3x2 + 3y = 2. Leave your answer correct to two…

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Q: Find the orthogonal trajectories on the sphere x2 + y2 + z2 = a2 of its intersection with the…

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Q: Calculate the double integral (x + y)²ex* - y² dx dy where R is the square with vertices (2, 0), (0,…

A: According to the given information, it is required to find the integral over R where R is square.

Q: Find the orthogonal trajectories of the family of hyperbolas xy = c

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Q: Find the sum of maximum and minimum values of the function f(x, y, z) = 4x + 8y + 12z on the elipse…

A: Using Lagrange Multipliers with Two Constraints

Q: Q1/ plot x2-y2=z (Elliptic paraboloid) in 3D.

A: Topic:- plot in 3-D

Q: Find the minimum of f(x,y) = 3x + 4y on the ellipsoid 6x2 + 2y² = 3. Leave your answer correct to…

A: Solution of the problem as follows

Q: 1. The solid bounded by the cylinder y = 9 – x² and the paraboloid y = 2x? + 3z².

A: In this question, we find the volume bounded by given surfaces. The surfaces: y=9-x2andy=2x2+3y2 The…

Q: 1. Compute SF · dr where F(x, y) = (y²,–x²) and C is the part of th parabola u = 12 from (-1 1) to…

A: First take dot product of f and dr Then put value of y in terms of x Integrate and raise limit of…

Q: Find F.dS if F (x, y, z) = 2xi+2yj+2zk and S is t he part of the paraboloid z = 8-x²–-y? lying above…

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Q: 1. Sketch carefully the solid enclosed by the three cylinders x + y* – 1,x² + 2² = 1, and y + z² =…

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Q: (8) Find the point(s) where the line r(t) = ti+(1+t)j+5k intersects the paraboloid z = x² + y?.

A: A detailed solution is given below.

Q: Find z dV, where E is the solid tetrahedron with vertices (0,0,0), (1,0,0), (0,2,0), and (0,0,4)

A: x varies from 0 to 1& y varies from 0 to 2 and z varies from 0 to 4.

Q: The shape of a redwood tree (without any branches) can be modeled by an upside down paraboloid, f(x,…

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Q: Numerically integrate y=x-X+4 from a-0 to b= 2 using single segment trapezoidal rule. O 12 0 8 0 6 O…

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Q: Find the minimum of f(x,y) = 5x + 2y on the ellipsoid 9x2 + 2y2 = 7. Leave your answer correct to…

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Q: Obtain the Solution x, y > 0, xy > 1 of 1 the PDE Ury Such that x+y 2у и 3 0, их on the hyperbola…

A: 1st we set up the initial value condition and draw the figure than set up PDE and solve it

Q: The surface area of the surface generated by revolving y= 1-x2 for 0<x<1 about the x - axis is S = […

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Q: Find the minimum of f(x,y) = 4x + 3y on the ellipsoid 4x2 + 2y2 = 6. %3D Leave your answer correct…

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Q: Evaluate 1 dv √x² + G where G is a solid that lies inside the cylinder x² + (y − 2)² = 4, above the…

A: Please see the attachment

Q: Find the maximum and minimum values of f(x, y, z) = x - z on the ellipsoid x² + 2y? + 22 = 1.

A: maximum=? minimum=?

Q: 2. Find the orthogonal trajectories of the family of parabolas y = cx O In(x² + y² ) = c O 2r? + y²…

A: Explanation of the answer is as follows

Q: Evaluate the triple integral.  (x2 + y2) dx dy dz; W is the pyramid with top vertex at (0, 0, 2)…

A: The given triple integral is,

Q: Find the minimum of f(x,y) = 7x + 3y on the ellipsoid 7x2 + 4y2 = 8. Leave your answer correct to…

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Q: Find the minimum of f(x,y) = 4x + 5y on the ellipsoid 9x2 + ly2 = 7. Leave your answer correct to…

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Q: Find the equations of the system of curves on the cylinder 2y = x² orthogonal to its intersections…

A: The given family of curves is got as the intersection of F(x,y,z)=2y-x2=0 with a one-parameter…

Q: Find the minimum of f(x,y) = 9x + 4y on the ellipsoid 9x2 + 2y2 = 4. Leave your answer correct to…

A: We have to find the minimum of f(x,y)=9x+4y on the ellipsoid 9x2+2y2=4.

Q: Find the absolute maximum and absolute minimum of the function f (x, y, z) = x³ + 2y along the curve…

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Q: 1. Determine the orthogonal trajectories of the hyperbola 3xy = 5 at point (2,5/6). Sketch es. %3D

A: Topic = Geometry

Q: Integrate G(x, y, z) = x2y2 + 4 over the surface cut from the parabolic cylinder y2 + 4z = 16 by the…

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Q: Find all points on the ellipsoid 2r² + 3y² + 4z² = 9 at which the plane tangent to the ellipsoid is…

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Q: 1 9. Evaluate dV;where E is the solid between the spheres of radius 1 (x² + y² + z²)³/2 E and 2…

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Q: Find the points on the surface z²2=xy+1 that are closest to the origin using LaGrange multipliers

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Q: Let F(x, y) that starts at (0, 0)and ends at (1, 2). (6æ? + 4y) 7 + (4x + 3) j. Calculate la F . dř,…

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