Consider the portion of the plane x + 2y + 3z = 12 that sits above the circle (x − 2)^2 + (y − 2)^2 = 4. Determine its surface area

Q: Sketch the surface..........CYLINDERS............. x2 + y2 = 4

A: x2+y2=4 Now, rewrite the above surface for the function as, z=fx,y. z=fx,y=4-x2-y2

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Q: Sketch the section of the surface at y= 0. z = V4 +x + y² 41 -8 -6 -4 -2 -4 6.

A: Let's find.

Q: Find the surface area of the plane ( 15x- 5z+20y=35) if it is in the first octant

A: Solution:-

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Q: Find the area of the surface. The part of the plane  x + 2y + 3z = 1  that lies inside the cylinder…

A: Compute the partial derivative as follows.

Q: Find the surface area of the plane ( 15x- ? 5z+20y=D35) if it is in the first octant

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Q: Find the surface area of the part of the plane 5x + 2y – z = 3 that lies above the box 3 <I< 5, 3<y<…

A: Here, z=f(x, y)=5x+2y-3, 3≤x≤5, 3≤y≤6. Now,          fx(x, y)=5   and   fy(x, y)=2. Thus, the…

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Q: Classify the quadric surface given by equation  and  determine its standard  form. x2 + y2 − z2 − 2x…

A: x2 + y2 − z2 − 2x − 4y − 4z + 1 = 0

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Q: Find the surface area of the plane 3x + 2 y + z = 6 that lies in the first octant.

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Q: classify the quadric surface given by equation and determine its standard form.−x 2 − y2 − z2 + 4x y…

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Q: Sketch the curve of intersection of the surfaces. The paraboloids z = x² + y° and z = 25 – x² – y² .

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Q: Find the area of the surface. The part of the plane 3x + 2y + z = 6 that lies inside the cylinder…

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Q: Find the area of the part of the sphere x+y +z = 16z that lies inside the paraboloid z =x²+y?.

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Q: Find the surface area of the plane ( 15x-5z+20y=35) if it is in the first ? octant

A: Solution

Q: Sketch the section of the surface at y = 0. z = 6r 4 2 -6 -4 -2 6. -4- -6 6r 4 2 -6 -4 -2- -4 4. 2.…

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Q: Find the area of the finite part of the paraboloid y = x² + z? cut off by the plane y = 16. [Hint:…

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Q: 7. Find the area of the portion of the plane z = 2y that lies directly above the circle x +(y-1)² =1…

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