1. Find the equation of the tangent plane to the surface by rly.v)- cu', vuu+ 2v > at the point (1, 3, 7). 2. Find the surface area of the parts of z=9-xy' that lies above or on the xy-plane. Sketch the surface S and evaluate.

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 an equation for the tangent plane to the surface z+1 = ry* cos(z) at the point (1, 1, 0)

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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: ind the equation for the tangent plane to the surface z = In(6x2 +9y2 + 1) at the point (0,0, 0).…

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

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Q: Find the equation for the tangent plane to the surface z=ln(4x2 +3y2 +1) at the point (0,0,0)

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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 angle of inclination 0 of the tangent plane to the surface at the given point. x² + y² =…

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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 at the given point. z = x2 - 2xy + y2,  (2, 3,…

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Q: Find the equation of the tangent plane at the point (1, 2, 7) to the surface given by x³ sin(z) +…

A: Consider a surface F(x,y,z)=0. Then the equation of the tangent plane to the surface F at the point…

Q: 7. Find the equation of the tangent plane to the surface: x² + y* -z =i, at (2, 1,2)

A: Given : x2+y2-z2=12z

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 for the tangent plane to the surface z + 1 = xy² cos(z) at the point (1, 1, 0)

A: The given equation is z+1=xy2cosz. The objective is to find an equation for the tangent plane to the…

Q: Find the angle of inclination 6 of the tangent plane to the surface at the given point. x2 + y2 =…

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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 equation of the tangent plane to x2 the surface z = 4 + y? at the point (2, –2, 5)

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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 angle of inclination of the tangent plane to the surface at the given point. x² + y² = 5,…

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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: Find the angle of inclination of the tangent plane to the surface x2+ y2+ z2 = 14 at the given point…

A: Consider the function fx,y,z=x2+y2+z2-14. Gradient of f can be obtained as follows. ∇fx,y,z=∂∂x,…

Q: Find an equation for the tangent plane to the surface z + 5 = xy° cos(z) at the point (5, 1, 0).

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Q: Consider the surface x^4+ 3xz + z^2+ cos( πxy ) = -2 and the point P0 ( -1, 1, 2) on that surface.…

A: Given the equation of surface x4+3xz+z2+cosπxy=-2 at point P0-1, 1, 2. The equation of tangent plane…

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: 12. Find the area of the surface generated when the curve y = ,on [1,2] is rotated about the x-axis.

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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 +…

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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: Find the equation for the tangent plane to the surface z = Vy -x at the point (2,3,1). Use a…

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

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

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 at the give h(x, y) = In √x² + y², (12, 16, In…

A: we have to find tangent plane

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: The equation of the tangent plane to the surface ye+z 0 at the point (0,-1,1) is az+by+cz 1. Which…

A: If  F(x, y,z)=0 is a three variable real valued function and generates the surface S, then the…

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: 3. Consider the surface sin (xy)+ cos (xz)+sin ( yz) =1. Find an equation for the tangent plane to…

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Q: 12. Find the area of the surface generated when the curve y =+,on [1,2] is rotated about the x-axis.

A: solution is given below...

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

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Q: Find the equation of the tangent plane to the surface z = xy at the point (1, 2, 2) and to the…

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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: 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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Q: Find the point(s) on the surface at which the tangent plane is horizontal. z = 3 - x2 - y2 + 4y (х,…

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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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