S is the surface with parametric equations x = Зи+ v, у — Зи— v, z = uv for (u, v) in the region D in the uv-plane bounded by the (x + y)²z² dS. Vx2 + y2 + 36 u°, v = 1, and u = 0. Evaluate curves v =

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

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Q: Find the area of the surface generated by revolving the parametric curve x = t, y = 2t² (0 ≤ t ≤ 1)…

A: Given, x=t,y=t2,0≤t≤1 The area of the surface generated by revolving the parametric curve about the…

Q: Find parametric equations of the normal line to the surface z = 4 +y? at the point (2, 3, 10) O x =…

A: To Find:  the parametric equations of the normal line to the surface  z = x24+y2 at the point ( 2,…

Q: Explain briefly how Vø relates to surfaces of constant o(x, y, x). Hence, use Vø to find points in…

A: For the surface of constants ϕx,y,z=k, the gradient vector ∇ϕx0,y0,z0 is orthogonal to the level…

Q: Consider the surface given by x²z+ 2yz2 = 3æy?. %3D (a) Find and (b) Find the tangent plane to the…

A: Surface given, x2z+2yz2=3xy2 ....(i) a)we have to find ∂z∂x  and ∂z∂y  Take equation (i) and…

Q: find a parametrization of the surface Circular cylinder band The portion of the cylinder y2 +(z -…

A: Given:The portion of the cylinder y2+(z-5)2=25 between the planes x=0 and x=10.

Q: Find the area of the portion of the cylindrical surface y = 4 – x² in the first octant that is…

A: Find your answer below below

Q: The area of the surface obtained by rotating the curve y = x2, 0 <x< 12 about the y-axis is

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Q: 4. Let II be the plane tangent to the implicit surface x²y° + e²= = 5+ 2y sin(z) at the point (-2,…

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Q: Sketch the section of the surface at y= 0. z = V4 +x + y² 41 -8 -6 -4 -2 -4 6.

A: Let's find.

Q: Consider the surfaces  z = x^2 +y^2   and z+ 2x+ 2y = 0 Find the projection of the curve on…

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Q: Asap Find the characteristic strips of the equation ap+yq-pq = 0 and obtain the equation of the…

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Q: 2. The surface area of the surface generated by revolving the curve y = x, -1 < x<1, about the…

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Q: Consider the surface z = x In y – x²y. (a) Show that Q = (1,1, –1) lies on this surface. (b) Find…

A: Consider the surface: z=xlny-x2y…

Q: S is the surface with parametric equations x = Зи+v, у — Зи-v, z = uv for (u, v) in the region D in…

A: Re-writting given integral in form of parametric equation as,∬F.n…

Q: find a parametrization of the surface. 1.The portion of the cylinder (x - 2)2 + z2 = 4 between the…

A: 1) Given information:

Q: Find the surface area of the solid obtained when the parametric curve x = −2cost; y=2sint for 0 ≤ t…

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Q: Find the slope of the tangent line at (-1, 1,5) to the curve of intersection of the surface z = x²…

A: According to question, we have, z = x2 + 4y2        .......(1)

Q: Find the area of surface x2 – 2y – 2z = 0 that  lies above the triangle bounded by the lines x = 2,…

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Q: 4. Consider the surface defined by the portion of the cone z = -Vx2 + y? that lies below the…

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Q: 5- Find the area of the surface generated by revolving the curve X= (y*/4) +1/ (8y²),1<y <2 ,about…

A: Given:function: x=y44+18y2Interval: 1≤y≤2To find : Area of surface generated by revolving the curve…

Q: 9ху. Use hyperbolic functions to parametrize the intersection of the surfaces x - y = 49 and z =

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Q: S is the surface with parametric equations x = 3u+v, y = 3u – v, z = uv for (u, v) in the region D…

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Q: 4. Consider the surface given by z = x x²esin y. (a) Find the equation of the tangent plane to z =…

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Q: 4. Find the area of the surface obtained by rotating the curve x²/3 + y>/3 = 1, 0 <y<1 about y-axis.

A: If the curve defined by the parametric equations x=x(t), y=y(t)  with a≤t≤b , is rotated about the…

Q: Find a parametrization of the curve. The intersection of the surfaces z = x^2 − y^2 and z = x^2 + xy…

A: Given : The surfaces z = x2 - y2 and z = x2 + xy - 1.   To find the parameterization of the curve.

Q: Find the areas of the surfaces generated by revolving the curve x= 2sqrt(4-y), 0≤y≤15/4

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Q: Let S be the surface obtained by revolving the plane curve 2x = /9 – y² about the y-axis.

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Q: a) Evaluate y° ds, where the curve C is the intersection between the surface z and the plane x = 3…

A: Integration problem...

Q: Find the surface area of the parametric surface F (и, v) — (2 сos(2и) + vcos(u), 2 sin(2u) +…

A: Here, we need to find the surface area of the parametric surface                               r→(u,…

Q: 3. Find a parameterization for the surface created by rotating the portion of y = x from x 1 to x =…

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Q: 4. Find the area of surface that is generated by revolving the portion of the curve I = 2/1- y,…

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Q: 3- Find the surface area of the solid obtained by rotating the curve z= 2/4- y; 0Sysabout the…

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Q: Suppose you head toward the xy-plane from the surface x? + y? – 2² = –1 at the point (1, 1, v3) by…

A: given,     x2+y2-z2=-1 at the point 1,1,3

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: Sketch the section of the surface at z = 0 on y = sinx in xy-plane on [0,27). y = sinx 4 56 1 3. 6…

A: The given equation of the curve is: y=sinx To draw the given equation on the x-y plane we need to…

Q: Find an equation for the plane that is tangent to the surface z = vy-x at the point (1, 2, 1).…

A: To find an equation for the plane that is tangent to the surface at the given point (1,2 1).

Q: Evaluate the surface integral. xyz dS, S is the cone with parametric equations x = u cos(v), y = u…

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Q: The region cut from the solid elliptical cylinder x2 + 4y2≤ 4 by the xy-plane and the plane z = x +…

A: Given that, z=x+2 , x2+y2≤4

Q: 1. Let S be the part of the plane 2.x – 2y + z = 1 inside the “cylinder" whose walls are given by…

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Q: Find the area of the surface that is generated by revolving the portion of the curve y = x2 between…

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Q: Find a set of parametric equalions for the surface formed when the curve y(1+z²) – 1 = 0 is revolved…

A: Find a set of parametric equations for the surface formed if the curve y1+z2-1=0 is revolved about…

Q: 3. Find the surface area of the surface generated by revolving the graph of the "curve" given…

A: The given parametric curve is: x=t,     y=t2,         0, 2

Q: - S is the surface with parametric equations x = 3u+v, y = 3u-v, z = uv for (u, v) in the region D…

A: We will find out the required value.

Q: Sketch the section of the surface at z = 0 on y = sinx in xy-plane on [0,2x]. y = sinx 1 3 4 5 1 1 2…

A: Let's find.

Q: Which of the following sets of parametric equations is for the surface obtained by rotating the…

A: For a fixed value of z, that is surface cut by a plane z=k it is a Circle, of radius 1/(10+k^2).

Q: The parametric representation of the surface x2 -8x + z2 = 0,0 < y 5 5 %3D is a) (u, v) = (4 cos u ,…

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Q: Evaluate the area of the surface generated by revolving the curve y = 2/a, from x = 0 to x = 3. y -…

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Q: (a) The part of the surface z = 1+ 3x + 2y² that lies above the triangle with vertices (0,0), (0,…

A: a) Given part of surface is  z=1+3x+2y2, which lies above the triangle with vertices (0, 0), (0, 1),…

Q: Consider the surface z = 4x2² + y² + 1. An equation for the tangent plane to this surface at the…

A: Given: z=4x2+y2+1