A surface is represented by the following multivariable function, f(x,y) = x+y³ - 3x- 3y+1 a) Calculate coordinates of stationary points.

Q: Find the equation of the tangent plane (in the form z = ax + by +c where a, b, c are constants) to…

A: Here we use the formula of  ∂f∂x(a,b)(x-a)+∂f∂y(a,b)(y-b)=0 tangent plane to the surface at a point…

Q: Find the point on the surface f(x,y)=x2+y2+xy-6x+8y at which the tangent plane is horizontal.

A: Given that: f(x, y)=x2+y2+xy-6x+8y

Q: The surface z=f(x,y) intersects the plane x-2 along the curve C which has equation of dy Find at the…

A: Given Data: The equation of the curve is: z=13y3-y2 The point at which derivative is required is: x,…

Q: 1. A surface is represented by the following multivariable function, r² + y² - 2ry – 6x – 3y + 4 a)…

A: Since, we have been given a surface that is represented by the followingmultivariable function given…

Q: The horizontal tangent plane of the surface z = 2x² – xy – y² + 6x – 6y – 2 is given by the equation…

A: Consider the given equation. z=2x2-xy-y2+6x-6y-2 Find the derivative with respect to x and y.…

Q: Describe the level surface F(x, y, z) = 0.…

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Q: The tangent plane to the surface with equation at the point where (x, y) = (1,0) has the equation z…

A: According to guidelines I solve the first question only.So kindly request you to repost the…

Q: Find the point(s) on the surface z = 3 − x2 − y2 + 6y, at which the tangent plane is horizontal.

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

A: The given function is It can be written as as the given function has both variables x and y.

Q: Find the slope of the tangent line to the curve that is the intersection of the surface z = x2 - y2…

A: Calculate point of intersection and differentiate it to get the answer

Q: find an equation for the plane that is tangent tothe given surface at the given point. z = √(y - x),…

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Q: Find the points on the surface y = 4 + xz that are closest to the origin. (х, у, 2) (smaller…

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Q: Given the surface z = In(-2x² + 5y² – xy). Find the directional derivative of the function f at…

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Q: Find the positively oriented simple closed curve C for which the value of the line integral C(y^3…

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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 points at which the following surface has horizontal tangent planes: x² + 2y² + z2 – 2x –…

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Q: Determine if the surface x^2 + y^2 +z^2 = 1 is tangent to the surface x^2 + y^2 + z^4 = 1 at…

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Q: Find the center of mass of the thin plate bounded by the y-axis and the lines y =x and y = 2 - x…

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Q: 4. Find both points on the surface xz – x2 – y? = 8 where the tangent plane is horizontal.

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Q: (b) Find the point that makes the tangent plane to the surface z = x² – xy + y? – 2x + 4y…

A: Find the partial derivatives with respect to x and y and set equal to zero. Solve for x in the…

Q: An equation of the tangent plane to the surface z = In(x - 2y) at (3, 1,0) is given by z = x + 2y- 1…

A: This question is related to three dimensions geometry.

Q: Find a formula for a functionf(x, y, z) whose level surface f= 3 is a cylinder of radius 5 centered…

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Q: Given a surface f(x,y) = -2x² + (-3)y“. Find the derivative in the direction of v = at the point…

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Q: Find the absolute maximum value of the function f(x, y) = 3x² + 2y² – 4y+1 | on the disk which has…

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Q: Find the plane tangent to the given surfaces at the specific point f(x, y) = x2 ln(2x+y) in (-1, 3)

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Q: Find the point on the surface f(x,y)=x2+y²+xy+21x+7y at which the tangent plane is horizontal.

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Q: Find all points on the surface at which the tangent plane is horizontal. (a) z = x³y² (b) z = x² −xy…

A: (a). Given the surface z=x3y2,the tangent lane at a given point is given by :…

Q: Find the positively oriented simple closed curve C for which the value of the line integral     (y3…

A: The line integral is  ∫C(y3 − y) dx − 9x3dy The expression for Green's theorem is  ∫CP(x,y) dx…

Q: Find the maximum and minimum values of a function F(x,y.z)3D8X+y+ z on the surface A

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Q: A surface is represented by the following multivariable function, 1 f(x,y) =x +y² - 2xy-6x-3y+ 4 a)…

A: Given function,fx,y=13x3+y2-2xy-6x-3y+4

Q: Find an equation of the tangent plane to the given surface at the specified point. z = 4x2 - y2 +…

A: The equation of tangent plane to the surface z=f(x,y) at any point (a,b,c) is…

Q: Find a point on the surface z = 3x^2 − y^2 at which the tangent plane to this surface is parallel to…

A: We need to find the Point on the surface of  z=3x2−y2 given tangent plane to this surface is…

Q: Find the point on the surface f(x,y)=x+y2+xy-24x+2y at which the tangent plane is horizontal.

A: We have to find the points for horizontal tangent plane.     According to our guidelines , We can…

Q: The equation of the tangent plane to the surface defined by z y exp(-x) at the point (0, 1, 1) is =…

A: equation of the tangent plane

Q: Let F(r, y, z) = 2x² + 14y? + 722. Find the equation to the tangent plane to the level of surface…

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Q: Find the point(s) on the surface z = 3x2 + 2y2 − 3x + 4y − 5, at which the tangent plane is…

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Q: Find the point on the surface  z=x2−y2  at which the tangent plane is parallel to the plane…

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Q: Find the point on the surface f(x,y)=x²+y²+xy+24x+13y at which the tangent plane is horizontal.

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Q: Find an equation of the tangent plane to the surface f(x, y, z) = x 2 + y 2 + xy − yz − xz + z 2 − 2…

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Q: Let f(x, y, z) = x^2 - y^2 – z. Describe the level surfaces.

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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 an equation for the plane that is tangent to the surface z = vy-x at the point (1, 2, 1).…

A: To find an equation for the plane that is tangent to the surface at the given point (1,2 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: Find the equation for the tangent plane to the surface z=In(9x2 + 5y2+1 O x+y = 0 z = 0 O x-y = 0 O…

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Q: (b) Find the point that makes the tangent plane to the surface z = x- xy +y-2x + 4y horizontal.

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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: Find the area of the surface f(x,y)= x² + 3y over the triangular domain bounded by the x-axis, the…

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Q: 13. Find all points on the surface at which the tangent plane is horizontal. 3,,2 (a) z = x°y ² (b)…

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