Find all equations of the tangent line to the common curve of the two surfaces with equations z = x² – y² – 2xy and z = x² + y² – 2xy – 2 at the point (2, -1, 7). 1.

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 the equation of the tangent plane to the surface y = 2x2 - z at the point %3D (0, -1,-2) y+2z =…

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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 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 the equation of the tangent plane to th surface 3x? + 5y? + 4z2 = 24 at the point (1, –1,2). 1.…

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Q: 4.) Find an equation for the plane tangent to the surface 9x² +4y² +9z² = 34 at the point (1,2,-1).

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

A: We know that the parametric equation of a tangent line to the curve of intersection of the two…

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 for the tangent line to the curve given parametrically by x(t) 2t, y(t) 4t2 +t+ 3 =…

A: we want to find the tangent lines to theparametric equations given byx=f(t)  y=g(t)The equation of…

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: 2. Find the slope of the tangent in the positive x-direction and y-direction to the surface z = 2xy…

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

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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 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: Find parametric equations for the tangent line to the curve of intersection of the cylinders x = 74…

A: given curves x2+z2=74 , y2+z2=74 , point 5,-5,7  to find parametric equations for the tangent line…

Q: Find an equation of the plane tangent to the surface sin(xyz) = at the point (T, 1,-)

A: sinxyz=12 at the point π, 1, 16. Consider, sinxyz=12⇒xyz=sin-112⇒xyz=π6⇒z=π6xy Differentiating…

Q: Find the slope of the tangent line to the curves cut from the surface z= 3x? +4y? -6 by planes…

A: The solution are next step

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 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: Find the equations of the tangent lines to the curve whose parametric equations are x = 2t2 – 4t +…

A: We find out dy/dx .then we find out value of t at given points and then find slope of tangent line…

Q: 12. Find an equation for the tangent plane to the surface given by 2xy = 2z2 - ryz at the point…

A: Use tangent plane formula

Q: Find an equation of the tangent plane to the surface at the given point. z = 5 - 2x - y, (3,-1, 1)

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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 for the tangent plane to the surface z=-8x2 -4y2 at the point (2,1,-30)

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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 surface z = 2y² – 3x² at the point (-3, -3, -9).

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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 the parametric equations of the tangent line to the curve of intersection of the surfaces x² -…

A: The equation of the tangent plane to the surface f(x, y, z)=0 at x0, y0, z0 is defined as: fxx0, y0,…

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: 3/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 an equation for the tangent plane to the surface z + 5 = xy" cos (2) at the point (5, 1, 0)

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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: 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 surface at the given point. x² + y² 7z² = 138, (-8, -9,…

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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: 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 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: 1)Determine the equation of the tangent line to the intersection of the surfaces x²-y=0 and y+z²=16…

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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 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 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: 3. Find the equation of the tangent plane to the surface in R³ defined by z = 2x² + y² at the point…

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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 )