X+ 3y and the planes Enclosed by the paraboloid z x= 0, y= 1, y = x, z = 0 13D

Q: This exercise refers to the hyperbolic paraboloid z = y – 3x2. Find an equation of the parabolic…

A: Solution is given below:

Q: find a parametrization of the surface. 1.The surface cut from the parabolic cylinder y = x2 by the…

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Q: 39. Find the surface area of the portion of the hyperbolic paraboloid r(u, v) = (u+ v) i + (u – v)…

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Q: 10. The part of the paraboloid x = y² + z² that lies inside the cylinder y² + z² = 9

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Q: Find the point on the sphere (x - 1)² +y² + (z + 9)² = 9 nearest to a. the xy-plane. b. the point…

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Q: Find the coordinates of the point (x, y, z) on the plane z = 3 x + 3 y + 2 which is closest to the…

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Q: find a parametrization of the surface. The paraboloid z = x2 + y2, z<=4 The paraboloid z = 9 - x2…

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Q: b) the region B in the first octant bounded by the surfaces z =r and r2 +y² + 2 = 1, and c) the…

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Q: Find the regions of the (x, y)-plane where the equation (1+ x) + 2xy; Əxðy + 2y? 2 + x xy? + (1 –…

A: Given equation is, 1+x∂2u∂x2+2xy∂2u∂x∂y+2y2∂2u∂y2+x2∂u∂x-xy2∂u∂y+(1-y)u=0 The equation…

Q: SSg z(x² + y²)do where S is the portion of the sphere x2 + y2 + z2 = 9 in the first octant that is…

A: Surface integral of a function f(x,y,z) Along the surface S given by z= g(x,y)…

Q: Find the area of the cap cut from the paraboloid y + z? = 3x by the plane x = 1.

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Q: Find the area of the surface cut from the paraboloid x² + y² -z = 0 by the plane z = 6. The surface…

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Q: This exercise refers to the hyperbolic paraboloid z = y – 6x². Find an equation of the parabolic…

A: Given:- z = y2 - 6x2 To find:- Equation of parabolic trace in plane x= 3

Q: The surface S formed by the point P(x,y,z) such that the distance from P to the point A(1.0,-1) is…

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Q: The surface with paramotik equations x= IV, y 3 V, 7 1+4u+5vis Select one O The plane x + bjy + z 1…

A: GivenParametric equation is x=u+vy=3-vz+1+4u+5vTo findPlane with x, y and z terms

Q: 2. || F. dš where F = 3x i+ 2z3+ (1- y²) k and S is the portion of z = 2 – 3y + x? Evaluate %3D that…

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Q: e |/| e² dV where E is enclosed by the paraboloid z = 4 + a?² + y², the cylinder Evaluate 2² + y² =…

A: Here we have to evaluate ∫∫∫Eez dV  where E is enclosed by the paraboloid z=4+x2+y2, the cylinder…

Q: F = (x² – y²,x, 2yz); C is the boundary of the plane z = 6 – 2x – y in the first octant.

A: Given, F=x2-y2,x,2yz Find the line integral ∮CF·dr in the following. Here C is the boundary of the…

Q: #5

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Q: III Find the area of the portion of the cylindrical surface y = 4- a2 in the first octant that is…

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Q: É = ( 2x³ + y³, y³ + 2³, 3y²z), S is the surface of the solid bounded by the paraboloid z = 1– x2 –…

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Q: AP where R is the portion of the ball of radius 1 in 4-dimensions with all coordinates r, y, z, w 2…

A: I = ∫∫∫R∫ dvwhere R = portion of unit ball with x, y,z,w≥0I = ∫01∫01∫01∫01 dx dy dz dw= ∫01∫01yo1 dz…

Q: The part of the cylinder y? + z2 = 81 that lies between the planes x = 0 and x = 5. (Enter your…

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Q: Find parametrizations The portion of the paraboloid z =-(x2 + y2)/2 above the plane z =-2

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Q: 5 + 2? + y, the cylinder Evaluate e dV where E is enclosed by the paraboloid z = E 2 + y? = 1, and…

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Q: 11. Evaluate ([(y+z³ )dS where S is the part of the paraboloid x = 4- y – z² that lies in front of…

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Q: 2 he volume of the region bounded above by the surface z =9-y and below ngle R: 0<x<3, 0sy<3. olume…

A: We have to find the following given conditions according to the given function information

Q: 16. Parabolic cylinder cut by planes Integrate а. g(х, у, 2) yz b. g(x, y, г) %3D V4y² + 1 V4y² + 1…

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Q: 14. Under the paraboloid z=x² +y2 and above the disk x +y² <9 for (x,y) in the first quadrant.

A: we have to find the volume

Q: Q1): Find the point (x, y, z) that lines on the plane x +y + 2z = 4 that is nearest to the origin.

A: This question can be solved using the concept of distance of point from a plane in three dimensional…

Q: he volumes of the solids generated by revolving the regions bounded by the graphs of the equations…

A: We have to find the volume about the given lines.

Q: Evaluate the surface integral.

A: We need to find the surface integral of

Q: 2x2 + 2y2 –1 that lies under the plane #5. Find the area of the part of the paraboloid z = z = 7.

A: given that z=2x2+2y2-1 and z=7 find the area of the part of the paraboloid

Q: 4. y=4-x² , y=3x and the x-y plane is given by the fol expresions.

A: We have to choose the correct option according to the given information

Q: lo. find a point in the plane x+2y+3z=13 nearest to the point (1,1) usung the methed of Lagrange's…

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Q: Find the intersection of the two planes with equations 3(x - 1) + 2y + (z + 1) = 0 and (x - 1) + 5y…

A: Dear,as per company guidelines we can answer only one question at a time, kindly post other question…

Q: Find parametrizations The portion of the sphere x2 + y2 + z2 = 36 between the planes z =-3 and z =…

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Q: (b) Integrate (x, y,z)=(y+z)+1 the paraboloid 4x - y-z -0 by the plane x 1. over the surface cut…

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Q: 3. Point Z is a centroid of the triangle VWY. If VZ = 42 cm, what is VX? %3D Y X W V

A: A triangle

Q: Find the points on the cone z = x° + y° that are closest to the point (1,-1,0) %3D +1

A: Given,

Q: 5) 2z dV, E is the solid enclosed by the cone % = Vr2 + y? and the E plane z 5

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

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Q: paraboloid z= 1 - (2x^2) -y^2 and plane z + x + y =4 find the shortest distance between them

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Q: 11. Evaluate ([(y² +z? )dS where S is the part of the paraboloid x=4-y -? that lies in front of the…

A: We will evaluate the given integral.

Q: Find parametrizations The portion of the paraboloid y = 2(x2 + z2 ), y&lt;=2, that lies above the…

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Q: Find the intersection of the two planes with equations 3(x - 1) + 2y + (z + 1) = 0 and (x - 1) + 8y…

A: The equation of the given planes are  3(x - 1) +2y + (z +1)=0...... (1) (x - 1) + 8y - (z +1)=…

Q: Find the area of the surface cut from the paraboloid x? + y +z=0 by the plane z= - 20. The surface…

A: The given equation of paraboloid is: x2+y2+z=0

Q: 3. Parameterize the following surfaces: (a) The part of the elliptic paraboloid x+y^2+ 2z^2= 4 that…

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Q: : The trace of the surface S x² Z = + 9. 4 in the plane z = 4 ||

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Q: 0lar coordinates to tind the volume: 2=6-R-y² and the paraboloid z=6-x-y² and 'ty² L4. 2. the plane…

A: For polar coordinates x^2+y^2 = r^2, dxdy = rdrdtheta x = rcostheta , y = rsintheta