Are there any points on the hyperboloid x² – y² – 2² = 1 where the tangent plane is parallel to the plane r+ y – z = 0?

Q: What is the equation of the plane to the surface z = e3y sin(3x) +2 at the point P ,0, 3 %3D O x- y…

A: The solution is given in the next step.

Q: Use Green's Theorem to compute y dx+(x³+3xy²) dy where C is the closed curve around the triangle…

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Q: Integrate G(x, y, z) = xyz over the surface of the cube cut from the first octant by the planes x =…

A: Here, the surface is in the first octant. Therefore, the integration is

Q: A point moves along the intersection of the elliptic paraboloid z = 9x? + 3y² and the plane.x…

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Q: Consider the PDE y Ur + a Uyy + Uz – Uy = r² + y? In what region of the xy-plane is this PDE…

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Q: Find an equation for the tangent plane to the surface z = 6x3y2 + 3y at the point P(1, -3). Hint:…

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Q: An equation of the tangent plane to the surface z = 4xy² + 3x²y² at the point (1, 1, 7) is: Select…

A: z= 4xy2+3x2y2F(x,y,z) =…

Q: Evaluate || f (x,y,z) dS where S is the portion of the sphere centered at the origin of radius two…

A: we have the equation of sphere x2+y2+z2=22s is the portion bounded between xy plane and z=1 in the…

Q: Consider x=h(y,z) as a parametrized surface in the natural way. Write the equation of the tangent…

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Q: a) Evaluate x²y? ds, where the curve C is the intersection between the surface z = := V1– y? and the…

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Q: Let H be the segment of the hyperbola x-y°= | Connecting (1,0) to (2, J3). Evaluate the line,…

A: Given  H be the segment of hyperbola x2-y2=1 connecting the points (1,0) to (2,3)  we have to…

Q: Determine the projection of the following surface on the xy plane. (xy trace) 4z-목 + =0

A: here first solve the given surface and then we trace it

Q: Find F. dr, where F(x, y) = (xy² + cos x)i+(x²y+sin y)j and C is the ellipse C x2 + 2y2 = 9,…

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Q: Find the area of the plane xtay-zt 10=0 that lies above the disk xy-plare

A: Given that, Area of plane is x+2y-z+10=0 It lies above the disk {(x,y)/x2+y2≤4} in x,y plane. The…

Q: Let (S) be the surface given by the following equation. x²+y² = 1+ z?. An equation of the tangent…

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Q: Find a parametric representation for the part of the cylinder y2 + z² = 36 that lies between the…

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Q: 2. Evaluate the triple in tegral where E is the y-2x2+2z20nd the plane y= 8. solid bounded by SI…

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Q: 2. Evaluate f, z³ /x² + y² + z² dV where E is the solid hemisphere that lies above the xy-plane and…

A: Solution:- equation of sphere having centre origin (0,0) and radius=1 x2+y2+z2=1…

Q: Are there any points on the hyperboloid r2 - y? – 22 = 1 where the tangent plane is parallel to the…

A: Given hyperboloid ;    x2-y2-z2=1  and equation of plne which is parallel to tangent plane  x+y-z=0

Q: What is the equation of the plane to the surface z = e3y sin(3x) +2 at the point P ,0, 3 O x - y -…

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Q: Consider x = h(y, z) as a parametrized surface in the natural way. Write the equation of the tangent…

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Q: a) Find the points at which the twisted cubic F(t) = ti + t} +tk intersects the plane 4.x +2y+z = 24…

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Q: Suppose f(x, y) satisfies the basic existence and uniqueness theorem in some rectangular region Rof…

A: Consider the given: Let the function f(x,y) satisfies the basic existence and uniqueness theorem in…

Q: 1) Find the volume of the solid that lies between the paraboloid z = 2x + 2y and the plane z = 8.…

A: Dear student, you didn't mention which question is to be solved so according to Bartleby guidelines,…

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 D the region in the first octant bounded by the hyperbolas (xy= 1, xy = 3), and the two planes…

A: Given Data xy = 1 xy = 3 y = 2x y = 4x Z = 4

Q: Let F (tanx + y)ĩ + (x + secy)j and C be the boundaries of the ellipse 9y=9 in the counterclockwise…

A: Given - F→ = tanx + yi^ + x + secyj^ and C be the boundaries of the ellipse x2 + 9y2 = 9 in the…

Q: Find the area of the part of the plane 3x + 3y + z = 9 that lies inside the cylinder x2 + y2 = 25.

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Q: 28. Show that the ellipsoid 2x² + 3y² + z² = 9 and the sphere %3D x? + y? + z? - 6x – 8y – 8z + 24 =…

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Q: 1 Find the surface area of the part of the hyperbolic paraboloid z = (x² - y²) that lies inside the…

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Q: 4. Compute |F- dš, where F = (y, –x,2z) and S is the surface of the sphere of radius 2, centered at…

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Q: What is the equation of the plane to the surface z = e3Y sin(3x) +2 at the point P,0, 3) O x- y + ez…

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Q: Integrate F =-(y sin z)i + (x sin z)j + (xy cos z)k around the circle cut from the sphere x2 + y2 +…

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Q: Calculate the positive value of m so that the x+y+2z=m plane is tangent to the spherical surface…

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Q: Find the region in the xy-plane in which the following equation is hyperbolic: ((x- y)? - 1]u + 2u,…

A: Given partial differential equation x−y2−1uxx+2uxy+x−y2−1uyy=0 We have to find the region in the…

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: Find a parametrization for the portion of the sphere x2 +y2 + z2 - 16 between the planes z =- 2/2…

A: we have been given a sphere x2+y2+z2=16 between the planes z=-22 and z=2

Q: Find all points where the surface z = xy e-* + 2y-) has a horizontal tangent plane. %3D O A. O B.…

A: Given the surface

Q: a) Evaluate ds, where the curve C is the intersection between the surface z = V1- y? and the plane r…

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Q: Which one of the following is the parametric equa- tions of the line that is normal to the surface…

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Q: Find the area of the part of the plane defined by 3z + 2y + z 12 that lies in the first octant.

A: Given equation of plane :  3x+2y+z= 12

Q: find ⌠⌠F*dS if F(x,y,z)=2xi+2yj+2zk and S is the paraboloid z=8-x^2-y^2 lying above the rectangle…

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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: 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: C is the intersection curve between the paraboloid z = x² + y? and the plane 6x + 8y – z = 21,…

A: Strokes theorem:

Q: The surface area of the part of the paraboloid z=x+y that lies under the plane z=2 is: Z=,

A: Surface area is given as A=∬D1+δzδx2+δzδy2dA

Q: 12. Let H be the hyperboloid where x² – y² + z² = 6. Find an equation for the tangent plane to H at…

A: As you asked only solution for Q12 so, I answered here only Q12

Q: yz ds where o is the part of the plane x + y+ z = 1 that lies in the first octant.

A: Given The given integral ∫∫σyzds over the region x+y+z=1 that lies in the first octant can evaluated…

Q: Use Stoke’s Theorem to evaluate the line integral ∮C(z2−y2)dx +(x2−z2)dy +(y2−x2)dz, where the curve…

A: Given equation of the curve is ∮C(z2-y2)dx+x2-z2dy+(y2-x2)dz ,the equation of the paraboloid…