The plane x = 1 intersects the paraboloid z = x 2 + y 2 in a parabola. Find the slope of the  tangent curve to the parabola at (1,2,5).

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

A: Given that   f(x,y)= z = x2-2xy+y2     So,  this can be rearrange as…

Q: Find the equation for the tangent plane at the point Po = (1,2, 2) on the surface x + 4y2 + 22 = 25.…

A: Equation of the Surface x2+4y2+2z2=25 point 1,2,2

Q: Show that the tangent lines at the points where the ellipse x² – xy + y² = 3 cross the x-axis are…

A: Explained below

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 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 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,…

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Q: Find an equation of the tangent plane to the surface at the given point. f(x, y) = x2 – 2xy + y²,…

A: Given: f(x,y)=x2-2xy+y2, (5,7,4).

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 at the given point. - 2xy + y², (3, 5, 4) eBook…

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

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

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

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 an equation of the tangent plane to the surface z = -! -3x? + 3y – 2x + 2y + 2 at the point (2,…

A: We have to find tangent plane

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: Find an equation of the tangent plane to the surface at the given point. f(x, y) = x² - 2xy + y²,…

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Q: Find an equation of the tangent plane to the surface at the given point. f(x, y) = x² – 2xy + y²,…

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

A: This question is based on finding equation of tangent plane.

Q: 3. z = (c

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Q: Find the tangent plane to the equation z 5a2 - 4y +5y at the point (5, 5, - 200)

A: The equation of the tangent plane to a surface  is given by fx(x-a)+fy(y-b)+fz(z-c)=0where (a,b,c) =…

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 the equation for the tangent plane to the surface z=-8x2 -4y2  at the point   (2,1,-36)

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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 surface z = 5y – 4x? at the point (4, 2, -44).

A: Given: Equation of surface is z=5y2-4x2 and a point -4, 2, -44. To find: Equation of tangent plane…

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: 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 tangent plane to the surface at the given point. f(x, y) = x2 – 2xy + y2,…

A:

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: Find the tangent plane to the equation z 4e- 4y at the point (8, 16, 4)

A: Let x0,y0,z0=8,16,4 be a point on the given surface. Then, the equation of tangent is…

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 the equation of the tangent plane to the surface -2² at the point y = 2x2 – (0, –1,2)

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Q: Find an equation of the tangent plane to the surface at the given point. 5 —х — у, z = 5 - (3, -2,…

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Q: Find an equation of the tangent plane to the given surface at the specified poin 8x2 + y2 - 7y, (1,…

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Q: Find an equation of the tangent plane to the surface at the given point. f(x, y) = x2 – 2xy + y2,…

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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: Find the equation of the plane tangent to the surface z x+y at the point (2, 1, 3). x-1

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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: 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 an equation of the tangent plane to the surface at the given point. f(x, y) = x2 - 2xy + y²,…

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

A: Finding partial derivatives with respect to x and y for finding plane equation.

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 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 the tangent line to the ellipse x^2+4y^2=8 parallel to the line x+2y=6.

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Q: Find the equation of the tangent plane and the normal line to the surface z=-2x -8y at the point…

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Q: Find an equation of the tangent plane to the surface at the given point. - . z = 8 —х — у, 3 (3, –4,…

A: Given plane is z=8−83x−y. We have to find the equation of tangent plane to the surface at the point…