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

Q: Find the surface area of the paraboloid z= 1 - (x2 + y?) that lies between the sphere x? + y? + z² =…

A: Given the region

Q: Sketch the section of the surface at x = 0. y? – 42? = 4

A: Given

Q: Consider the sphere r? + y? + 22 = 9. Please find the equation of the plane tangent to this sphere…

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Q: A) || Jx2 + y2 dA , R is the disk x2 + y? < 9

A: We have to use polar coordinates here.

Q: Find the area of the segment of a sphere formed by revolving the graph of       y = √(r2 − x2) , 0 ≤…

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Q: Evaluate fff 1- x2 - y2-z2 dx dy dz where V is the volume of the sphere x? + y? + z2 = a? by…

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Q: Write the sphere equationil odi lo anoitaupo ontemeeg bas Totoov bnif (d) x2 + y? + z2 + 2x - 4y –…

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Q: Sketch the surface created by 4.r2 + 9y? + 3622 = 36. %3D

A: Given,4x2+9y2+36z2=36 Simplify equation (i) as x29+y24+z21=1  .....(i) Intercepts along x,y,z…

Q: Use cos(t) and sin(t), with positive coefficients, to parametrize the intersection of the surfaces…

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Q: Find the area of the part of the sphere x² + y? + 2? = 12z that lies inside the paraboloid 2 % = x²…

A: Topic = Application of integration

Q: Use traces to sketch and identify the following surface 25x² + 4y? + z² 100.

A: Given: The surface 25x2+4y2+z2=100.

Q: Determine whether the statement is true or false. If D is the disk given by x2 + y2 s 49, then 49 x2…

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Q: cribe the surface with equation x + y° + z? + 8x + 4y + 2z – 43 = 0 surface is a sphere with center…

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Q: Consider the following equation of a sphere. What is the result of adding the coordinates of the…

A: We first complete the square for the sphere.…

Q: Find the point on the sphere x +y +z = 4 that is close O A. V11 V11 9. V11 (유 O B. 11 V11 V11

A: Solution of the problem as follows

Q: Which one of the following surfaces is the aph of f(z, y) = y -2 ? 3..

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Q: Evaluate fff(r +y²+y dV, "AP where 2 is the solid hemisphere (half of the sphere) enclosed by x +y…

A: Converting into spherical  coordinates

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

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Q: sketch the given surface. x = 1 + y 2+ z2

A: sketch the given surface. x = 1 + y 2+ z2

Q: Find the center and radius of the sphere. * + + 5z +x+y+z= 4 5x +

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Q: 8. Find the surface area of the part of the sphere x2 + y? + 22 : = 4z that lies inside the…

A: The solution is given as

Q: Find the area of the part of the sphere x2+y2+z23D 9z that lies inside the paraboloid z =r+y?. a.…

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

A: Given: x2 + y2 − z 2= 1

Q: Let E be the part of the unit sphere r² + y²- = 1 where z > vx² + y². Calculate 22 dA.

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Q: Find the area of the part of the sphere x2 + y? + z² = 4z that lies inside the paraboloid z = x2 +…

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Q: Consider the parametric surface S given by the portion of the sphere x +y² +z² = 4 where z 2 1.

A: In this question, we have to parameterize the surface in cartesian coordinates and then find the…

Q: Let S be the sphere 2 + y² +2²=9 oriented outwards, an F = (5x, 7z, -3y) Evaluate: (6₂ F. ds. The…

A: let S be the sphere x2+y2+z2=9 oriented outwards and F=5x,7z,-3y evaluate ∫∫SF·dS

Q: Find the point lying on the intersection of the plane x + y +z = 0 and the sphere x2 + y? + z? = 25…

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Q: dA, where K is the disk r + (y 2 +?

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Q: Evaluate the exact area of the surface obtained by rotating the circle x2 + y² = r² about the line y…

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Q: Find the area of the surface when y = vx, from (4, 2) to (9, 3) is rotated about the x-axis.

A: Surface area formula for rotating about x-axis is S=∫2πydS where dS=1+dydx2dx

Q: Use sine and cosine to parametrize the intersection of the surfaces x² + y² = 16 and z = 4x³. r(t) =

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Q: Find the area of the surface given by r(u, v)=9ui-vj+vk, where 0≤u ≤2 and 0 ≤ y ≤4. O 45√2 O 38/2 O…

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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: Evaluate fff(x +y +:' dV, where a is the solid hemisphere (half of the sphere) enclosed by x +y+ =1…

A: Here in the given question, find the integration of the given function:∭Dx2+y2+z232dVWhere Ω is the…

Q: Which of the following is a non-orientable surface? O a. all the other choices are orientable O b.…

A: orientable surface -  The surface for which we can define clockwise consistently.

Q: Which surface below is an elliptic paraboloid? O x^2 + y^2/4 - z^2 = 1 O z = -sqrt(x^2 + y^2) z =…

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Q: If a parametric surface given by ri (u, v) = f(u, v)i + g(u, v)j + h(u, v)k and -3 <u < 3, –4 < v<…

A: We solve this

Q: (a) Find the point of intersection between the curv urve r(t) = (cos(at), sin(at), t²) and the…

A: We’ll answer the first part of this question since due to complexity. Please submit the question…

Q: Find the area of the portion of the sphere x2 + y² + inder x2 + y? = 6y. %3D

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Q: Find the area of the part of the sphere x+y +z = 16z that lies inside the paraboloid z =x²+y?.

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

A: Solution

Q: 3. Find the area of the surface cut from the paraboloid x? + y +z = 2 by the plane y = 0.

A: Here we have to find the area of the surface cut from the paraboloid x2+y+z2=2 by the plane y=0.

Q: Which surface has the following equation? x2 – 2y = 32 O Cylinder O Plane Paraboloid Hynerboloid

A: Please refer to the image below

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…

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Q: Parametrize the intersection of the surfaces using t = z as the parameter. (If there are multiple…

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Q: Let y ==a and z =. Find the intersection of these х x2 surfaces.

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Q: Find the surface area of a quarter of the sphere x? + y2 + z2 = 4.

A: The equation of a sphere centered at x0, y0, z0 is defined using the formula: x-x02+y-y02+z-z02=r2,…

Q: Use Gauss's D.T. to evaluate SSA.ds where Ã=x'i+y°§+7f qud S is the , surdace of the sphere x+j+z²=…

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