Does the the paraboloid z = 1 – 2x² - - y² have a tangent plane at some – x + y + z = 1?

Q: 2. Prove that fo r*dr + xydy = -+- where C2 is the line segment from (1,0) to (0, 1) by using…

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Q: Find the points on the surface xy + yz + zx - x - z2 = 0 where the tangent plane is parallel to the…

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Q: Find a parametrization of the vertical line passing through the point (9, 5, 0) using t = z as a…

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Q: Find the equation of the tangent plane to the surface 4xe^yz+xz^2−7x^3y= 5 at(1,0,1).

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

A: Given: x2+y2=4

Q: Let L denote the intersection line between the planes 2x-y-3z=4 and 2x+y-z=2 A) Determine a…

A: Solution of the system of equation will give the equation of the line of intersection.

Q: Find the equation for the tangent plane to the surface z=ln(4x2 +3y2 +1) at the point (0,0,0)

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Q: Find the equation of the plane tangent to the surface G(x,y, z) = 2x² - y² – 3z2 = -4 at P = (-2,…

A: Given surface is                                                G(x, y, z): 2x2-y2-3z2=-4 we have to…

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

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Q: A point moves along the intersection of the elliptic paraboloid z = x² + 3y² and the plane y = 1. At…

A: Point moves along the intersection of the elliptic paraboloid z=x2+3y2 and the plane y = 1. We have…

Q: Find a parametrization for the curve y = Vx with terminal point (0, 0) using the angle 0 in the…

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Q: Give a parametrization, including the appropriate u- and v-bounds, for the portion a cylinder of…

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Q: A point moves along the intersection of the elliptic paraboloid z = a2 + 3y? and the plane y = 1. At…

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Q: 14) Find the points on the surface xy- z2 = 1 that are closed to the origin. %3D

A: To find the point on the below surface that is closed to the origin. xy−z2=1

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

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Q: Find a parametrization of the hyper-boloid of two sheets (z2/c2)-(x2/a2)-(y2/b2)=1

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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: Show that the line normal to the surface xy + z = 2 at the point (1, 1, 1) passes through the…

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Q: Find the points on the surface ry + yz + zx – x - 22 = 0 where the tangent plane is parallel to…

A: Given surface is  Fx, y, z=xy+yz+zx-x-z2 and we have to find the points on this surface where the…

Q: Find the equation for the tangent plane to the surface z= 7x2. 10y² at the point (2, 1, 18). O 2x +…

A: Equation for the tangent plane to the surface z=f(x, y) at the point (a, b, f(a, b)) is given by

Q: (a) Between 1 and the disk x²+ (1+x² +y*) (b) Between % = 1 and the entire xy-plane. (1+x* + y?)*

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Q: Suppose that the plane tangent to z = f(x,y) at (-2,3,4) has equation 4x + 2y + z = 2. Estimate…

A: As the given plane tangent to z=f(x,y) at (-2,3,4) is  4x+2y+z=2, that is z=2-4x-2y thus the…

Q: Find an equation of the tangent plane to the surface z = In(x - 2y) at the point (3, 1,0) %3D

A: Given that, z = ln (x - 2y) we have to find the equation of tangant at point (3, 1, 0).

Q: Are there any points on the hyperboloid x 2 − y 2 − z 2 = 1 where the tangent plane is parallel to…

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Q: The tangent plane to the elliptic paraboloid z = 2x2 + y² at the point (1, 1, 3) is %3D 1) 8x + 6y +…

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Q: Find an equation of the tangent plane to the surface zx + 2xy + 3yz3 = 6 at a point in the…

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Q: At what point on the paraboloid  y= x^2 +z^2is the tangent plane parallel to the plane x+2y+3z=1 ?

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Q: Find a parameterization for the hyperbolic paraboloid z = z – y².

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Q: Find the equation of tangent plane to the surface x^2 + 2y^2 + 3z^2 = 21 which is parallel to the…

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Q: Find a point on the surface z = 3x^2 − y^2 at which the tangent plane to this surface is parallel to…

A: We need to find the Point on the surface of  z=3x2−y2 given tangent plane to this surface is…

Q: Find the point (x, y, z) on the surface z = 2x2 - y where the tangent plane is parallel to the plane…

A: We have to find the point (x, y, z) on the surface z = 2x^2 - y^2 where the tangent plane is…

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: Find the equation of the tangent plane to the surface f(x,y)=In(4x²-2xy-y²) at the point P(-1,-1,0).

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Q: The tangent plane equation of the level surface z =-x² – 3y² at point (2,2,-16) is. O a.…

A: Given: The tangent plane equation of the level surface z=-x2-3y2 at point (2,2,16)

Q: Find an equation of the plane tangent to the surface xy z2 = 2 at the point (2, 1, -1). %3D

A: Given that XY3 Z2 =2 And point (2, 1,-1).

Q: Find the orthogonal trajectories of the conicoid (x + y)z = 1 of the conics in which it is cut by…

A: Given:The equation of conicoid is (x+y)z=1The system of the plane is x-y+z=K, where k is…

Q: A point moves along the intersection of the elliptic paraboloid z = 9x + 4y and the plane y = 4. At…

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Q: Find the equation of the tangent plane to the surface 3D1 16 at the point (1,-3,2) O a. 2x+4y-3z=12…

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Q: Find the tangent plane to the elliptic paraboloid z = x² – 2y at the point (1,1,1). - O A. z = 2x –…

A: Given that: z=x2-2y2      and point is:   (1, 1, 1)

Q: Find the equation for the tangent plane to the surface z=In(9x2 + 5y2+1 O x+y = 0 z = 0 O x-y = 0 O…

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Q: Find a parametrization of the curve of intersection of the surfaces z = x² – y² and z = x² + xy + 1.

A: The given curves are z=x2-y2 and z=x2+xy+1 To find the intersecting curve : Let us equate both the…

Q: Are there any points on the hyperboloid x² – y² – 2² = 1 where the tangent plane is parallel to the…

A: By see this solution

Q: The tangent plane to the elliptic paraboloid z = -2x - 7y? at the point (-3, -4) is

A: Consider the provided question, The equation of the tangent plane to the elliptic paraboloid at the…

Q: Bounded by the paraboloid z = 10 – 3x? – 3y2 and the plane z = 4 (using polar coordinates)

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Q: Find the equation of the tangent plane to the surface z = xy at the point (1, 2, 2) and to the…

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Q: Find the equation of the tangent plane to the surface xy + 2yz + 3zx = 11 %3D at the point P (1, 1,…

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Q: Find a parametrization for the intersection of the surfaces: z = x2 + y2 and  x2 + 4y2 = 1

A: Find the parametric representation for the intersection of the given surfaces.

Q: Find an equation of the tangent plane to the surface z=−1x^2+1y^2+3x−1y+3 at the point (5, 5, 13).…

A: Given the equation of surface is:                               z=-x2+y2+3x-y+3 We nee to find the…

Q: Find the equation of the tangent plane to the surface y = 2x2 (0, –1, 2) z at the point O y+ 4z = 7…

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Q: 14. Find a point on the surface z = 3x- y at which the tangent plane is parallel to the plane 6x +…

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