Suppose you need to know an equation of the tangent plane to a surface S at the point P(2, 1, 4). You don't have equation for S but you know that the curves (2 + 2t, 1 – t, 4 – 5t + t?) r2(u) = (1 + u², 2u³ – 1, 2u + 2) r(t) %3D both lie on S. Find an equation of the tangent plane at P.

Q: 4. Find the equations of the line tangent to the intersection of the surfaces z = x´ + 2y and

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Q: Find an equation for the tangent plane to the surface 22 – xy? = 0 at the point (1, 3, 3).

A: Given that At point (1,3,3) Take, Now to find the divergence of f, The divergence at point…

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 the equation of the tangent plane to the surface 2= 42 + 3y+7zy at the point (0,-1,3).

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

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Q: of the tangent plane to the surface z=e-4x/17ln(1y) at the point (-3, 4, 2.808).

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Q: Find the equation of the plane tangent to the following surface at the given points. x² +…

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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: z = In (x² + y²) at point Po(1,0, 0).

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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) xy-2x

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

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Q: Find the equation of the tangent plane to the surface y = 2x2 – z2 at the point (0, –1, –1) y+ 4z =…

A: We have to find

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: Find the equation of the tangent plane to x2 the surface z = 4 + y? at the point (2, –2, 5)

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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 plane tangent to the following surface at the given point. z = 6 - 4x2 - y2;…

A: By using equation of tangent plane for surface, we calculate the required tangent plane.

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 at the given point. x^2 + 3y^2 + 4z^2 = 20, P =…

A: The equation of the tangent plane can be calculated by using the formula…

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=−1x2+3y2−3x+1y+1 at the point (2, 2, 5).

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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: 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 the equation for the tangent plane to the surface z = - 9x - 7y at the point (2, 1, - 43). O A.…

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Q: Find an equation of the tangent plane to the surface at the given point in the figure below.

A: Consider the given:…

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 an equation of the tangent plane to the given surface at the specified point. z3 бх2 + у2 - 7у,…

A: Solved below...

Q: find an equation for the plane that is tangent tothe given surface at the given point. z = 4x2 + y2,…

A: It is given that, z = 4x2 + y2, at the point (1, 1, 5) We have to find the equation of tangent…

Q: If the equation of the tangent plane to x2+y2-147z²=0 at (1,1,/2 / 147) is x+ay+Bz+y=0, then a+ß+y=

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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 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: 22 2 Find the equation of the tangent plane to the level surface xy*z? (– 1, – 1, – 2) = 4 at the…

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

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Q: 4. Let S1 : x + y – 2z +1 = 0 and S2 : x² + y – z = 0 be two surfaces. Find symmetric equations of…

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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 surface at the given point. 4x2 + 2y2 + 5z2 = 177, P =…

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

A: Given that: z = 2x2 + y2 - 5y, (1, 2, -4)

Q: 4. Find the equation of the tangent plane to the level surface x4 + yz – yz² + 5x = 0 at 3

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Q: Find the equation of the plane tangent to and the line (in symmetric form) normal to the ellipsoid…

A: Given:   x2+ 4y2 +8z2 = 48 Point : ( -2 , 3 , -1)

Q: Let ƒ(x, y) = 2x + 3y - 4. Find the slope of the line tangent to this surface at the point (2, -1)…

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Q: Find the equation of the tangent plane to the surface z = x² +y² + 1 at the point (1,1,3). Write the…

A: use the equation of tangent  plane for the given surface.

Q: Find an equation of the tangent plane to the given surface at the specified point. z = 6x² + y² -…

A: This question is based on finding equation of plane to the given surface at a point.

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: 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 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 )