Find an equation of the tangent plane to the surface at the given point. x² + y2 + z2 = 33, (1, 4, 4) Find symmetric equations of the normal line to the surface at the given point.

Q: find equations for the(a) tangent plane and(b) normal line at the point P0 on the given surface.3.…

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

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 an equation of the tangent plane and a normal line to the surface z = In Vx2 + y2 at the point…

A: Given that: z=lnx2+y2

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 given surface at the specified point. 2. (-16, 4, -1)

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Q: a) Find an equation of the tangent plane to the surface at the given point. xyz = 15, (1, 3, 5) b)…

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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: Find the equation of the tangent plane to the surface - 8x3 + 7y³ + 3xy at the point (2,0, 64).

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Q: Find the equation for the tangent plane and the normal line at the point Po(1,1,3) on the surface…

A: Given problem:- Find the equation for the tangent plane and the normal line at the point Po(1,1,3)…

Q: Find an equation of the tangent plane to the given surface at the specified point. = 4(x – 1)2 + 3(y…

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

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Q: 6. Find an equation of the tangent plane to the surface z = y² – x² at the point (-4, 5, 9).

A: Recall: Equation of the tangent plane to the surface z=f(x,y)  at (x0,y0,z0) is        fxx-x0 +…

Q: Find the angle of inclination of the tangent plane to the surface at the given point. x² + y² = 5,…

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

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Q: Find the equation for the tangent plane and the normal line at the point Po(3,3,1) on the surface x…

A: To find an equation for the tangent plane and the normal line at the point (3,3,1).

Q: Find equations for the a) tangent line and b) normal plane to the curve made by the intersection of…

A: Given The given surfaces are 3x2y+y2z=-2 and 2xz-x2y=3.  The given point is 1,-1,1.

Q: Q3/Find the equation for the tangent plane and normal line to the surface Z = 9-x² + y² at the point…

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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…

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Q: Find the equation for the tangent plane and the normal line at the point Po(3,2,3) on the surface 2x…

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

A: Given: The function is fx,y=yx, 1,5,5. The objective is to find an equation of the tangent plane to…

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 surface y ln xz2 = 2, at the given point (e, 2, 1) and…

A: Given: ylnxz2=2 at the given point e,2,1

Q: Find the equation of the tangent plane to the surface of the equation z = x2 + y2 - 2xy on the point…

A: Equation of tangent plane

Q: find equations for the(a) tangent plane and(b) normal line at the point P0 on the given surface. 2z…

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Q: 9. Find an equation for the tangent plane and the normal line to the surface xy + yz + zx = 5 at the…

A: f(x,y,z)=xy+yz+zx-5=0,  at  (1,2,1)now we differentiate above equation with respect to x,y,z…

Q: Find the equation for (a) the tangent plane and (b) the normal line at the point Po(4,0,4) on the…

A: The above problem is solved.

Q: Find the equation for the tangent plane and the normal line at the point Po(2,3,1) on the surface 3x…

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Q: 3. Find the equation of the tangent plane and the equations of the normal line to the surface z = In…

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Q: Find the equation of the tangent plane and normal line to the surface at the given point. x2 z = 9…

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Q: 7. Find the equation of the tangent plane to the surface: x +y² -z² 1 z, at (2, 1, 2)

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Q: (a) Find an equation of the tangent plane to the surface at the given point. x2 + y2 + z2 = 14, (1,…

A: We have to solve given Questions.

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: 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 the equation for (a) the tangent plane and (b) the normal line at the point Po(8,0,8) on the…

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

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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 of the tangent plane to the given surface at the specified point. 5Vy Z = (-1, 1,…

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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: 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 z = √(9 − x2 − y2), at the given point (1, 2,…

A: The surface given is Fx,y,z=√(9 -x2 -y2) -z =0. The derivative of the surface coordinates with…

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

A: GivenSurface F(x,y,z)=x2+y2+z2-3=0Point of…

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

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