1. Let f(x, y) = ay + y?. (a) Describe the a cross-sections of the surface f. Sketch three of these cross-sections. (b) Describe the y cross-sections of the surface f. Sketch three of these cross-sections. (c) Find the equation of the tangent plane to f at the point (2, 2).

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 an equation of the plane tangent to the following surface at the given points. zexy; (1,0,1)…

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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: 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: An equation for the tangent plane to the surface : = (xty at the point P(1, 1, 4) is a) 8x + 8y -: =…

A: Equation of a tangent to the surface z=f(x,y) at point (a,b,f(a,b)) is given by…

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 of the tangent plane to the surface defined by the equation zf(x, y) + 2³ = 3 at…

A: The given surface is:zf(x, y)+z3=3The point is (-1, 2, 3)

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

A: Given point is (1, 2, 1).

Q: Find the equation of the tangent plane to the surface z = f ( x , y ) = x 3 − 2 x y + 5 y 2 at P (…

A: Given: The equation of the surface  z=f(x, y)=x3-2xy+5y2. The point P2, 1, 9.

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 an equation of the tangent plane to the given surface at the specified point. z = x sin(y – x),…

A: From the given equation: z=xsin(y-x) And Px,y,z=8,8,0 Let, f(x,y,z)=z-xsiny-x As we know that, The…

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 an equation for the tangent plane to the surface f(x, y) = e^xy + 4x^2 + 4y^2 at the point…

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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: At which of the points below is the tangent plane to the surface x² – 2y + z + yz = 2 vertical?…

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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 of the tangent plane to the given surface at the specified point. z = 2(x – 1)2 +…

A: Equation of tangent plane to the given surface ' z=fx,y' at point x0,y0,z0 is…

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 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: (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 z = + y? x2 4 at the point (2, -2, 5) x- 4y -…

A: We have to solve

Q: Find an equation of the tangent plane to the given surface at specified point. a) z = e*y +…

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

A: Here, the surface is: z=ln(x-3y) To find the equation of the tangent plane at the point (7,2,0).…

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 an equation of the tangent plane to the given surface at the specified point. z = 4(x - 1)2 +…

A: We have equation of the form     z= f(x, y)  And we have to find equation of tangent plane to the…

Q: 9. Show that the sum of the T-, y-, and z- intercepts of any tangent plane to the surface VI + Vỹ +…

A: Given, Gradient of the surface at any point (x0,y0,z0) is given by,

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

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Q: Find an equation of the tangent plane to the given surface at the specified point. z2 = x2 + y?,…

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Q: Find the equation of the tangent plane to the surface 2 = r - 2r'y+ 2r y at the point where x = 1…

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Q: Find an equation of the tangent plane to the given surface za² + y² +1 at (1,1,3).

A: Given equation of the surface is  z=x2+y2+1 We have to find the tangent plane of the given surface…

Q: f(z, y) = (z + 2)* - 2(y - 1) - 5. (2,3, 3)

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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: 3. (a) Find the equation of the plane tangent to the surface given by f(x, y) = 2xª+2y^+7xy at the…

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Q: Find the equation for the tangent plane to the surface z= In (7x + 10y + 1) at the point (0,0,0).

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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 of the tangent plane to the surface z = 24 3z+4y at the point (4,3, 1).

A: Use equation of tangent plane

Q: Find the equation of the plane tangent Z= x2+ Y2 at point P (1,2,5) to the surface

A: Equation of tangent plane on the surface z=f(x,y)  at the point (a,b,c)  is given…

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 the equation of the tangent plane to the given surface at the point (0,-1,-2). y = L - O + 2z =…

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Q: Find the equation of the tangent plane to the surface x?+ Qy?-322=3' at (2-1,1) x²+ 2y 2-322=3'at…

A: Equation of a tangent plane

Q: Find an equation of the tangent plane to the given surface at the specified point. 2x2 + y? – 9y,…

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Q: Find an equation of the tangent plane to the given surface at the specified point. z= e(x^2)-y2,…

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Q: Find an equation of the plane tangent to the surface f(x, y) = xy² – 5x at the poin (1, 2, –1).

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

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