Calculate the volume of the region inside the cylinder x +y = 4, above the XY-planea...
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4. Conpute the volume of the region s inside the cylinder z2 +y2 = 1, between the paraboloid :-x2 + y2-2 and the plane z + :-4
4. Conpute the volume of the region s inside the cylinder z2 +y2 = 1, between the paraboloid :-x2 + y2-2 and the plane z + :-4
Let E be the solid that lies inside the cylinder x^2 + y^2 = 1,
above the xy-plane, and below the plane z = 1 + x. Let S be the
surface that encloses E. Note that S consists of three sides: S1 is
given by the cylinder x^2 + y^2 = 1, the bottom S2 is the disk x^2
+ y^2 ≤ 1 in the plane z = 0, and the top S3 is part of the plane z...
The region above the xy-plane that is inside both the sphere 2? + y2 + x2 = 4 and the cone 22 + y2 – 322 = 0, has density at a point given as f (x, y, z) = x2 + y2 What is the mass of the region?
All of 10 questions, please.
1. Find and classify all the critical points of the function. f(x,y) - x2(y - 2) - y2 » 2. Evaluate the integral. 3. Determine the volume of the solid that is inside the cylinder x2 + y2- 16 below z-2x2 + 2y2 and above the xy - plane. 4. Determine the surface area of the portion of 2x + 3y + 6z - 9 that is in the 1st octant. » 5. Evaluate JSxz...
EXAMPLE 4 Find the volume of the solid that lies under the paraboloid z 5x2 - 5y2, above the xy-plane, and inside the cylinder x2 + y2-2x (x-1)2 + y2=1 or r 2 cos 8 SOLUTION The solid lies above the disk D whose boundary circle has equation x2 +y2x or, after completing the square, In polar coordinates we have x2 +y Thus the disk D is given by and x-r cos(), so the boundary circle becomes 2r cos(), or...
1 point) Find the volume of the wedge-shaped region (Figure 1) contained in the cylinder x2 + y2-4 and bounded above by the plane z = x and below by the xy-plane. z=x FIGURE 1
1 point) Find the volume of the wedge-shaped region (Figure 1) contained in the cylinder x2 + y2-4 and bounded above by the plane z = x and below by the xy-plane. z=x FIGURE 1
4. (14 points) Using polar coordinates, set up, but DO NOT EVALUATE, a double integral to find the volume of the solid region inside the cylinder x2 +(y-1)2-1 bounded above by the surface z=e-/-/ and bounded below by the xy-plane.
4. (14 points) Using polar coordinates, set up, but DO NOT EVALUATE, a double integral to find the volume of the solid region inside the cylinder x2 +(y-1)2-1 bounded above by the surface z=e-/-/ and bounded below by the xy-plane.
Q3(a) Let W be the region above the sphere x2 + y2 + z2 = 6 and below the paraboloid z = 4 - x2 - y2 as shown in Figure Q5(a) below: Z=4-x-y? x2 + y + z = 6 Figure Q3(a) (i) Find the equation of the projection of Won the xy-plane. (ii) Compute the volume of W using polar coordinates. [16 marks] (b) Using double integral in polar coordinates, compute the following: $$*** (2x+3y) dedy [7 marks]...
Please try helping with all three questions.......please
1 point) Integratef(x, y, z) 6xz over the region in the first octant (x,y, z 0) above the parabolic cylinder z = y2 and below the paraboloid Answer Find the volume of the solid in R3 bounded by y-x2 , x-уг, z-x + y + 24, and Z-0. Consider the triple integral fsPw xyz2 dV, where W is the region bounded by Write the triple integral as an iterated integral in the order...
(1 point) y2 and below the paraboloid 8xz over the region in the first octant(x, y, z 0) above the parabolic cylinder z Integrate f(x, y, z) Answer:
(1 point) y2 and below the paraboloid 8xz over the region in the first octant(x, y, z 0) above the parabolic cylinder z Integrate f(x, y, z) Answer: