If the gradient of f is Vf = x³ } – zỉ+ 2yx k and the point P = ( surface f (x, y, z) = 0, find an equation for the tangent plane to the surface at the point P. (7, –7, 10) lies on the level

Q: 4. Find an equation of the tangent plane to the surface xyz = sin(x + y + z) at (1, −1,0).

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Q: find equations for the(a) tangent plane and(b) normal line at the point P0 on the given surface.5.…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: If the gradient of f is ∇f=y3j−xi+zyk and the point P=(−8,6,2) lies on the level surface f(x,y,z)=0,…

A: To find the equation

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: 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 equations for the(a) tangent plane and(b) normal line at the point P0 on the given surface. cos…

A: Given,

Q: Find the angle of inclination 6 of the tangent plane to the surface at the given point. x2 + y2 =…

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

A: Tangent plane to f(x, y) at (x0, y0) is given by below:

Q: If the gradient of f is Vƒ = z j - yi – 2xzk and the poi f(x, y, z) = 0, find an equation for the…

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Q: Picture attached. Thanks in advance!

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Q: 4. Find an equation of the tangent plane to the surface x = u? + 1,y = v³ + 1,z = u + v at the point…

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Q: Find a unit normal to the surface x'y + 2xz = 4 at the point (2,-2,3).

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Q: Find for the equations for tangent plane and normal line at P,on the given surface 2 х2 — Зху — у?…

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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 slope of the tangent line to the curve of intersection of the surface z = x + y' with the…

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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: If the gradient of f is Vƒ = 3x i + z² j+ 2yz k and the point P = (4, –6, –9) lies on the level…

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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 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: Find parametric equations for the line tangent to the curves of intersection of the surfaces xyz =1…

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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 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: What is the equation for the tangent plane to the surface z = 4x°y2 + 2y - 2 at the point P(1, -2,…

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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 the equation of tangent plane and normal lines of the surface: f(x, y, z) = 5x² + 4 y2 +z³-9 at…

A: Here we have to find the equation of the tangent plane and normal lines of the surface:…

Q: Find the equation of tangent plane and normal lines of the surface: ( x, y, z) = 5x^2 +  4y^2 + z^3…

A: We have to find the equation of tangent plane and normal lines of the surface: f(x,y,z)=5x2+…

Q: Find the equation for the tangent plane to the surface z = Vy -x at the point (2,3,1). Use a…

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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 an Equation for the tangent plane and normal line at the points Po on the given surface. x +…

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Q: If the gradient of f is ∇f=yj⃗ −xi⃗ −4zyk⃗  and the point P=(−7,−8,−3) lies on the level surface…

A: an equation for the tangent plane to the surface at the point P

Q: Find an equation of the tangent plane to the given surface at the specified point. 3Vy Z = VY, (-1,…

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

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Q: Find an equation of the tangent plane to the given surface za² + y² +1 at (1,1,3).

A: Given equation of the surface is  z=x2+y2+1 We have to find the tangent plane of the given surface…

Q: 4. Find an equation of the tangent plane to the surface x = u? + 1, y = v + 1, z = u + v at the…

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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: Find the plane tangent to the surface given by the function f(x, y) = (x² + y) sen(x - y) + 2x in…

A: Tangent plane  z= f(x0,y0)+fx (x-x0)+fy(y-y0)

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

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Q: Find an equation of the tangent plane and symmetric equations of the normal line to the surface zx2…

A: Given the equation of the surface can be rearranged in the form F(x,y,z)=0 zx2-xy2-yz2-18=0 Here,…

Q: Find an equation for the tangent plane to the surface given by f(x,y)=÷(4x² – 2y²) at the point…

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Q: Find the slope of the tangent line to the curve that is the intersection of the surface z=x² - y…

A: The details solution is given below

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: find equations for the(a) tangent plane and(b) normal line at the point P0 on the given surface. x2…

A: Consider the function fx,y,z=x2+y2-z2-18. ∇fx,y,z=fx, fy, fz=2x, 2y, -2z. At 3, 5, -4, ∇f3, 5,…

Q: Solve for an equation of tangent plane and parametric and equations of normal line to the given…

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Q: Find the point(s) on the surface at which the tangent plane is horizontal. z = 3 - x2 - y2 + 4y (х,…

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Q: Determine the equation of the tangent plane and normal line to the surface at the given point.…

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