ns: Find the tangent plane to the surface of x2 + z² = y² + 9 at (1, –1,3). 3

Q: Find the equation of the tangent plane to the given surface at the specified point. z=xsin(x+y),…

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Q: find the tangent plane to the surface z = Vy-x at the point (1,2,1)

A: Equation of tangent plane is z-c = df/dx(x-a)+df/dy(y-b) at point (a,b,c)

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: Find the points on the surface xy + yz + zx - x - z2 = 0 where the tangent plane is parallel to the…

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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: 1. Use the tangent plane to the surface f(x, y) = x² + y? mate f(1, 2). at the point P(-1,1,2) to…

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Q: find an equation for the plane that is tangent tothe given surface at the given point.11. z = ln (x2…

A: To find an equation for the plane that is tangent to the given surface at the given point. Given…

Q: The area of the surface obtained by rotating the curve y = 22 x + 1, 0 < x < 44 about the x-axis is

A: Consider the given curve. y=22x+1 in the interval 0≤x≤44 The problem requires to find the area of…

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 of the tangent plane to the surface S : za? – xy – yz = 18 at the point (0, –2, 3).…

A: We know that an equation of the tangent plane to the surface Fx, y, z at the point x0, y0, z0 is…

Q: Find the tangent plane and normal line to the surface f (r, y) = In (2r + y) at the point (-1,3,0).…

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: The area of the surface obtained by rotating the curve y = x2, 0 <x< 12 about the y-axis is

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Q: Find the equation of a tangent plane to the surface of z = eª cos(y) at the point P(0,0, 1).

A: Consider the provided question, Hello. Since your question has multiple parts, we will solve first…

Q: Find the area of the surface obtained by rotating the curve }=2,3 from z = 0 to z = 1 about the…

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Q: The horizontal tangent plane of the surface z = 4x – xy – 2y – 2x – 8y – 3 is given by the equation…

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

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Q: Find an equation of the tangent plane to the surface x = u² + 1, y = v³ + 1, z = u + v at the point…

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Q: Find the equation of the tangent plane to x² the surface z = + y? 4 - at the point (2, 3, 10) x + 6y…

A: The equation of the tangent plane to a surface f(x,y,z) is given by:

Q: Find an equation for the plane tangent to the surface e z = x cos(xz) – y at the point (2, 1,0).

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Q: Find the point on the surface f(x,y)=x2+y2+xy-16x-27y at which the tangent plane is horizontal.

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Q: Find an equation of the tangent plane to the surface z = 2a2 + 1y – la – 3y – 1 at the point (5, 3,…

A: Equation of Tangent Plane to the surface F(x, y, z) = 0 at point (x0, y0, z0) is given by ∇F(x0, y0,…

Q: Let F(x, y, z) = 15x? + 12y2 + 10z?. Find the equation to the tangent plane to the level of surface…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

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: Find the equation of the tangent plane to the surface determined by z'y' + z – 25 = 0 at z = 4, y =…

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Q: Find the point on the surface f(x,y)=x²+y²+xy-17x+9y at which the tangent plane is horizontal.

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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 the point on the surface f(x,y)=x2+y2+xy-26x+29y at which the tangent plane is horizontal.

A: For Given surface f(x,y) The slope of horizontal tangent plane is equal to zero.

Q: H.W: find the tangent plane to the surface z = Vy -x at the point (1,2,1)

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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 an equation of the tangent plane to the surface z= z + 2y² at the point P(1, 1, 3). Nind th…

A: We’ll answer the 1st question since we answer only one question at a time. Please submit a new…

Q: Consider the surface x2 + y2 − 2xy − x + 3y − z = −4 and the point P(2, −3, 18). Determine the…

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Q: Find the sum of the x-intercept, y-intercept, and z-intercept of any tangent plane to the surface…

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Q: Find an equation of the tangent plane to the given surface at the specified point z = √√√xy, (3, 3,…

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Q: Find the equation of the tangent plane for the surface z = xy at the point (-1,2,-2) O z=x-2y+2…

A: The equation of tangent plane for the surface z =f(x,y ) at point (m,n,f(m,n)) is given as:

Q: Find the tangent plane to the surface z = 9 – x* – y? at the point (1, -3, –1).

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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: 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 area of the surface that is generated by revolving the portion of the curve y = x2 between…

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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 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: Find an equation of the tangent plane to the surface given implicitly by z= sin(zy) at the point (,…

A: A tangent plane to a surface is a plane that just touches the surface at a single point. The…

Q: Find the equation of the tangent plane to the surface x^2e^z+xyz+y= 3 at the point (1,2,0)

A: Find the equation of the tangent plane to the surface x^2e^z+xyz+y= 3 at the point (1,2,0)

Q: Find an equation for the plane tangent to the surface e'z = x cos(xz) – y at the point (2, 1, 0).

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Q: Consider a surface defined by F(, y, z) = 0 whose gradient is (cos(Tx), z? e", 2ze"). The equation…

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Q: Find an equation of the tangent plane to the given surface at the specified point. z = (xy)^1/2,…

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

Q: 30. The equation of the tangent plane to the surface z = x? – 2y² at x = 1, y = 0 is (а) 2 — : 2т —…

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Q: Determine the equation of the tangent plane to the surface z=x - 3xy + y at the point P (2, 1, 3).…

A: Solution

Q: Find an equation of the tangent plane to the surface z = xy at (1,2,2).

A: The given surface can be written as F(x, y, z)=0, where F(x, y, z)=xy-z

Q: The area of the surface obtained by rotating the curve x = y2 - In(Vy), 1sys2 about the x-axis is

A: The given curve is: x=14y2-lny  ;      1≤y≤2 Therefore: dxdy=y2-12y

Q: Find an equation of the tangent plane to the given surface at the specified point. z = V xy, (2, 2,…

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