Which of the following is the equation of the tangent plane to the surface z=x2 - x+3y² +y at the point P(1, 1,4) ? (a) x+7y =6 (b) x+7y-z=4 (c) 3x+5y=8 (d) 3x+5y-z= 4 (e) x+7y+z=12

Q: Find the equation of the tangent plane (in the form z = ax + by +c where a, b, c are constants) to…

A: Here we use the formula of  ∂f∂x(a,b)(x-a)+∂f∂y(a,b)(y-b)=0 tangent plane to the surface at a point…

Q: The equation of the tangent plane to the surface x² 8 at the point (-2, 1, 3) is Select one: 1/2…

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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: Find the slope of the tangent line at the point (1,−2,−3) on the curve of intersection of the…

A: Given surface is z=5-4x2-y2 The slope of tangent line to the curve that is the intersection of the…

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

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Q: Find the equation for the tangent plane to the surface Z =-8x² - 3y2 at the point (2 1, -35). O 2x +…

A: We can find the answer as below

Q: Find an equation of the tangent plane to the surface z = -2z² – 2y?- lz 2y+ 3 at the point (5, 1,…

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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: Find the equation of the tangent plane to the surface y = 2x2 - z2 at the point (0, –1, –1) %3D | |

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Q: 1. Give an equation of the tangent plane to the surface z= In(4y – x) at the point (3,1,0).

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Q: Find the equation of the tangent plane to the surface =1 16 at the point (1,-3,2) O a. 3x-2y+z=24 O…

A: Given: x24+y29+z216=1 x,y,z=1,-3,2. Simplify the equation.…

Q: Find an equation of the tangent plane to the surface z = x2 + y2 + 3 at the given point( 2, 1, 8).

A: Known fact: Let F(x,y,z) be the surface which is differentiable at P(x0, y0, z0). then the equation…

Q: Find an equation of the tangent plane to the surface z=8/2x+4y at the point (2,1,1). z=

A: Please see the explanation below

Q: Let F(x, y, z) =7x2+8y2+13z2. Find the equation to the tangent plane to the level of surface F(x,…

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Q: Find an equation of the tangent plane to the surface at the given point z= 5x - xy3+y2,     (1,1,5)

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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: In this question we have to find a point on the surface at which the tangent is perpendicular to the…

Q: The points on the surface x2−2y2−3z2 = 33 at which the tangent plane is parallel to the 8x+4y+6z=5…

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Q: The equation of the tangent plane to the surface x² z² at the point (-2, 1, 3) is Select one: + 2y.…

A: To find the equation of tangent plane.

Q: Find the points on the surface 6x² + y² – 3z² = 4 where the tangent plane to the surface is parallel…

A: We need to find points of intersection.

Q: /Find the equation for the tangent plane and normal line to the surface Z = 9-x² + y² at the point…

A: Given eq. of surface z=9-x2+y2 at the point 1,2,4             (1)

Q: Write parametric equations for the tangent line to the curve of intersection of the surfaces x +y +z…

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Q: Find parametric equations for the normal line to the surface x2 + 9xyz + y² = 11z2 at the point (1,…

A: Given:- x2+9xyz+y2 =11z2  To find:- Equation of normal line to the given surface at point (1,1,1)

Q: Find an equation of the tangent plane to the surface x2 + 2y? + 3z2 = 6 at the point (1, 1, 1). O A.…

A: As we know that the equation of the tangent plane: nxx-x0+nyy-y0+nzz-z0=0 Given:…

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: An equation for the tangent plane to the surface z + 3 = xy cos (2) at the point (3, 1, 0) is:

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

A: The equation of the tangent plane to the surface Z=fx,y atthe point a,b,fa,b is given by…

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: The equation of the tangent plane to the surface x2 at the point (-2, 1, 3) is Select one: +2y z-3…

A:

Q: An equation of the tangent plane to the surface x = 3 y2 - z2 at the point (8, –-2,2) is: %3D (A) (x…

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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: The equation of the tangent plane to the surface x² 8 at the point (2,-1, 3) is Select one: O x-2…

A: In this question, we want to find the equation of the tangent plane to the given surface.

Q: Let C be the curve on the xy-plane that is the projection of a horizontal cross-section of the…

A: Given surface is,yz=ln(x+z) zxy=1x+z(1+zx)y-1x+zzx=1x+zzx=1y(x+z)-1 Take the derivative with respect…

Q: Find an equation of the tangent plane to the given surface at the specified point. z2 = x2 + y?,…

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Q: An equation of the tangent plane to the surface x = 3 y2 - z2 at the point (8, -2, 2) is: (A) (x –…

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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: 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: 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: 4. Determine all points on the surface x² + 2y² + 3z² + 2xy + 2yz = 1 in which the tangent plane of…

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Q: Find the equation of tangent plane to the surface x² + 2y? + 3z2 = 21 which is parallel to the plane…

A: Topic- equation of tangent to surface

Q: Find an equation of the tangent plane to the surface z = 24 3z+4y at the point (4,3, 1).

A: Use equation of tangent plane

Q: Find the equation of the tangent plane to the surface 2x^2 -xz + y^2 -zy = -5 at the point (1, 3, 4)

A: First we find out partial derivative at given point and then find the equation of the tangent plane…

Q: Find an equation of the tangent plane to the surface x-xyz 56 at the point (-4,5,2). Select one:…

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Q: Write parametric equations for the tangent line to the curve of intersection of the surfaces x =…

A: To find: The parametric equations for the tangent line to the curve of the intersection of the…

Q: the tangent plane of the surface [ x^2+y^2+z^2=14] at the point (1,3,2) O 3 x-6y + 4z = 28 2x+6y-4z…

A: Given problem:- the tangent plane of the surface [ x2 +y2+z2=14] at the point (1,3,2)

Q: Compute the equation of the tangent plane to the surface: y = 1 - x2 - 2z2 At the point (0, 1, 0)

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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…

A: