5. (10 points) Find an equation of the tangent plane to the surface given by z2 – 2x2 – 2y² = 12 at the point (1, –1, 4)

Q: 4. Find equations of the tangent plane and the normal line to the surface yz = arctan(2x+z) at the…

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Q: 32 – x² – 3y² at the 5. Find the equation of the tangent plane to the surface z = point (2, –1, 5).

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Q: Find an equation of the tangent plane to the surface z = x^3- y^2 + 12x + 2y at the point (1, 2, 5).

A: Given: z = x^3- y^2 + 12x + 2y (1, 2, 5)

Q: Find a point on the surface x+4y--z² =1 where the tangent plane is parallel to the plane x+4y- z =…

A: we need to find gradient of given surface to know about direction of normal vector to tangent plane

Q: 25 at the point ( 1, -1, 2 ).

A: Given that : The surface  8x2+y2+4z2 = 25 , point = ( 1, -1, 2 ).

Q: Find an equation of the tangent plane to the surface at the given point. x2 + y2 + z2 = 21, (1, 4,…

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Q: Find an equation of the tangent plane to the surface xyz = 10, at the given point (1, 2, 5), and…

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Q: Find all equations of the tangent line to the common curve of the two surfaces with equations z = x²…

A: follow next step

Q: Find the slope of the tangent line to the curve of intersection of the graph of z = 2x2 + 3xy + 2y2…

A: We need to find slope of the tangent line.

Q: 7. Find the equation of the tangent plane to the surface: x² + y* -z =i, at (2, 1,2)

A: Given : x2+y2-z2=12z

Q: 6. Find the equation of the tangent plane to the surface: ==√√4-x²-2y², at (1,-1, 1)

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Q: 2. Find the equation of the tangent plane to the surface z = 3++ at point (-4, 3).

A: Topic- application of derivatives  Tangent to surface

Q: 2. Find the slope of the tangent in the positive x-direction and y-direction to the surface z = 2xy…

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Q: 5) Find the equation of the tangent plane to the surface exyz= x + 2y + 3z at the point (3,-1,0).

A: Find tangent plane to the surface

Q: Find the equation of the tangent line to the common curve of the two surfaces with equations z = x²…

A: Please check step 2 for solution.

Q: Find the equation of the tangent plane to the surface z = 4 号+ゾ + y² at the point (2, -3, 10)

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Q: Find an equation of the tangent plane to the surface z = 2x² + 1y² + læ + ly – 2 at the point (2, 5,…

A: This question is based on 3d geometry.

Q: #5. Find an equation of the tangent plane to the surface with the equation 12x z = x²y*. y at the…

A: The given equation of the surface: z=x2y4-12xy Therefore: f(x, y)=x2y4-12xy Now:…

Q: Find an equation of the tangent plane to the surface z = 16 − x2 − y2 at the given point (2, 2, 8)…

A: To Determine: Find an equation of the tangent plane to the surface z = 16 − x2 − y2 at the given…

Q: 1. Find an equation of the tangent plane to the surface of z = sin(x - 2y) at the point (7,2,0).

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Q: Find equation of the tangent plane to the given surface at the specified point. 5x^2+3y^2+8z^2,…

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Q: Find the equation for the tangent plane to the surface x2 - 5xyz + y² = 7z2 at the point (-1, -1,…

A: Simplify the given equation of the surface in the form F(x,y,z)=0. x2-5xyz+y2=7z2x2-5xyz+y2-7z2=0…

Q: Find the equation of the tangent plane to the surface y = 2a2- z2 at the point (0,-1, 1)

A: Here is the solution

Q: 2 2 the equation of the tangent plane to the surface x² + y² + y² +2²= -1 at the point (2, -3, 4)

A: I am attaching image so that you understand each and every step.

Q: 12. Find an equation for the tangent plane to the surface given by 2xy = 2z2 - ryz at the point…

A: Use tangent plane formula

Q: Find an equation of the tangent plane to the surface at the given point. z = 5 - 2x - y, (3,-1, 1)

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Q: Find the equation for the tangent plane to the surface z=-8x2 -4y2  at the point   (2,1,-36)

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Q: Find an equation of the tangent plane to the surface x² + 2y² + z² = 175 at the point (5, -5, 10). O…

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Q: 4. Find an equation of the tangent plane to the surface z=- xy+8 at the point (1,1,-10) ху — 2х

A: Equation of tangent plane is: {df(x0,y0)/dx} (x-x0)+{df(x0,y0)/dy} (y-y0)-(z-z0)=0

Q: find the slope of the tangent to the curve of intersection of the surface 3z=√36-9x²-4y² and the…

A: Consider the surface 3z=36-9x2-4y2and the plane x=1 at the point 1,-2,113.The objective is to find…

Q: Find an equation of the tangent plane to the surface z = 2y² – 3x² at the point (-3, -3, -9).

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Q: Find equations of the normal plane and tangent line to the curve of intersection of the surfaces…

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Q: Find the equation of the tangent plane to the surface 4 =1 at the point 16 9 (1,-3,2) O a.…

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Q: 9) Find a point on the surface z = 8 – 3x2 – 2y² at which the tangent plane is perpendicular to the…

A: Given, Surface, z=8-3x2-2y2 at which the tangent plane is perpendicular to the line…

Q: Find an equation of the tangent plane to the surface at the given point. z = 8 – (3, –4, 4)

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Q: 3. Find the equation of the plane tangent to xyz + x² – 2y² +z' =14 at (5,–2,3)

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Q: 3. Find an equation of the tangent plane to the surface z = 2xy + 4y xy-2x at the point (1,1,-6)

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Q: Find an equation of the tangent plane to the surface at the given point. x² + y² 7z² = 138, (-8, -9,…

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Q: Find the equation of the tangent plane and the normal line to the surface x +y = 6xyz +8z2 at the…

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Q: Find an equation of the tangent plane to the surface at the given point. x² + y2 – 5z2 = 140, (-8,…

A: We will solve the problem

Q: Find the equation of the tangent plane to the surface z = ly² – lz² at the point (-2, 0, -4). 4x+0

A: Given   z=y2-x2 We have to find equation of tangent line at the point(-2,0,4)

Q: 1)Determine the equation of the tangent line to the intersection of the surfaces x²-y=0 and y+z²=16…

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Q: Find the equation of the tangent plane to the surface y = 2x - z at the point (0, -1,-2) y+2z = -5…

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Q: b) Find the equations of Tangent plane and Normal line of the surface: z3 + xyz – 2=0 at Po(1,1,1)

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Q: 7.) Find an equation of the tangent plane to the surface, x y(2z-3), at the point P(4,4,2)

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Q: Find an equation of the tangent plane to the surface x2 + y2 + z2 = 9 at the given point (1, 2, 2)…

A: Given equation: x2+y2+z2=9 Consider the given equation, fx,y,z=x2+y2+z2-9=0

Q: Find an equation of the tangent plane to the surface at the given point. xy2 + 3x – z2 = 56, (5, -3,…

A: Given:   xy2 + 3x - z2 = 56  Point ( 5 , -3, 2 )

Q: Find an equation of the tangent plane to the surface at the given point. - . z = 8 —х — у, 3 (3, –4,…

A: Given plane is z=8−83x−y. We have to find the equation of tangent plane to the surface at the point…