3. Find the equation of the tangent plane to the surface in R³ defined by z = 2x² + y² at the point (1, 1, 3).

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 horizontal tangent plane of the surface z = 2x² – xy – y² + 6x – 6y – 2 is given by the equation…

A: Consider the given equation. z=2x2-xy-y2+6x-6y-2 Find the derivative with respect to x and y.…

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 the slope of the tangent line to the curve that is the intersection of the surface z = x2 - y2…

A: Calculate point of intersection and differentiate it to get the answer

Q: Find the general equation of the tangent plane to the surface x2 + y2 −2xy −x + 3yz = −4 at the…

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

A:

Q: Find an equation of the tangent plane to the surface S : za? – xy – yz = 18 at the point (0, –2, 3).…

A: We know that an equation of the tangent plane to the surface Fx, y, z at the point x0, y0, z0 is…

Q: Find an equation of the tangent plane to the surface z = x2 + y2 + 2 at the given point (1, 3, 12)

A: Given surface, So

Q: Find the equation of a tangent plane to the surface of z = eª cos(y) at the point P(0,0, 1).

A: Consider the provided question, Hello. Since your question has multiple parts, we will solve first…

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 point(s) on the surface z = x2 − xy + y2 − 2x − 2y, at which the tangent plane is…

A:

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

A:

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

A:

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 given surface at 'the specified point. Z =2x²+y&-5y and…

A: The equation of a tangent plane to the surface f(x,y,z) at the point x0 , y0 , z0 is calculated…

Q: Find the equation for the tangent plane to the surface x- 5xyz+ y = - 7z at the point (- 1, -1, -…

A:

Q: Find the points on the surface 2a2 + ly² + 522 = 1 at which the tangent plane is parallel to the…

A: We will use the following method for finding the two required point.

Q: Find an equation of the tangent plane to the surface x = u² + 1, y = v³ + 1, z = u + v at the point…

A:

Q: Find an equation of the tangent plane to the surface z=−2x^2+3y^2−x+3y+1 at the point (1, 1, 4)…

A: We have to find the  equation of tangent plane

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: Find an equation of the tangent plane to the surface at the given point.   z= y/1+6x…

A:

Q: Find an equation of the tangent plane to the surface 4x^2 + 9y^2 − z^2 = 14 at P = (2, 1, 4).

A: Given,4x2+9y2-z2=14at P=(2,1,4)

Q: Find an equation of the tangent plane to the surface z= z + 2y² at the point P(1, 1, 3). Nind th…

A: We’ll answer the 1st question since we answer only one question at a time. Please submit a new…

Q: Find an equation of the tangent plane to the given surface at the specified point z = √√√xy, (3, 3,…

A:

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: 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 an equation of the tangent plane to the given surface at the specified point. z = 4(x - 1)2 +…

A: We have equation of the form     z= f(x, y)  And we have to find equation of tangent plane to the…

Q: 4. Find the equation of the tangent plane to the surface ew + In(xz) - evz = 0 at the point (1,0,…

A:

Q: Find an equation of the tangent plane to the given surface at the specified point. f(x,y) =…

A:

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).

A:

Q: Find the equation of the tangent plane to the surface x^2e^z+xyz+y= 3 at the point (1,2,0)

A: Find the equation of the tangent plane to the surface x^2e^z+xyz+y= 3 at the point (1,2,0)

Q: Find an equation of the tangent plane to the surface at the given point. z = x2 + y2 + 4, (1,2, 9)

A: We know that the equation of tangent plane to the curve z=f(x,y) at point (a,b,c) is

Q: Find an equation of the tangent plane to the surface at the given point. h(x, y) = In V x2 + y², (6,…

A:

Q: Find an equation of the tangent plane to the surface at the give h(x, y) = In √x² + y², (12, 16, In…

A: we have to find 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: 3. Find an equation of the tangent plane at P = (0, 3, –1) to the surface with equation ze" + elz+1)…

A:

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 given surface at the specified point. = In(x - 3y),…

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Q: Find an equation for the tangent plane to the surface z = 3y^2 − 2x^2 + x at P(2, −1, −3). Express…

A: Let's find equation of tangent plane.

Q: Find an equation of the tangent plane to the given surface at the specified point. z = y In(x), (1,…

A:

Q: Find an equation of the tangent plane to the given surface at the specified point. z= e(x^2)-y2,…

A:

Q: Find an equation of the plane tangent to the surface f(x, y) = xy² – 5x at the poin (1, 2, –1).

A: Consider the provided question, Hello. Since your question has multiple parts, we will solve first…

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

A:

Q: Find an equation of the tangent plane to the surface z = √(x2 + y2), at the given point (3, 4, 5).

A: We have given equation z=x2+y2 First we rearrange the equation of the surface into the form fx,y,z=0…

Q: Find an equation of the tangent plane to the surface z = xy at (1,2,2).

A: The given surface can be written as F(x, y, z)=0, where F(x, y, z)=xy-z

Q: Find the equation of the tangent plane to the surface z = 3 e^(x−y) at the point (4, 4, 3)

A: We find the equation of the tangent plane to the surface z = 3ex-y at the point (4, 4, 3).

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

A:

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: