Ans: 2x(x- a)y' = y(3x- 2a) 7. The cubics cy² = x² (x – a) with a held fixed.
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- Solve these prism and cylinder exercises. Where necessary, round the answers to 2 decimal places unless otherwise specified. A solid right cylinder 9.55 centimeters high contains 1910 cubic centimeters of material. Compute the cross-sectional area of the cylinder.The base of a solid is the region in the first quadrant bounded by the x-and y-axes and the graph of y=((x-2)^2)/(2(x+1)).For the solid,each crosssection perpendicular to the x-axis is a rectangle whose height is three times its width in the xy-pane. What is the Volumeof the solid?Find dy/dx if ylnx + y^2 = 0. A rectangular solid with a square base has a surface area of 534.5 square centimeters. Whatdimensions will produce a solid with maximum volume? Use calculus and verifythat it gives a maximum volume.
- D. Find the exact volume of the solid formed by revolving R2 about the x-axis. (No calculator approximations)The base of a solid is the region in te first quadrant bounded by the graph of y=1-x/3 and the x-and y-axes. For the solid, each cross-section perpendicular to the x-axis is a square. What is the volume of the solid?use Taylor’s formula for ƒ(x, y) at the origin to findquadratic and cubic approximations of ƒ near the origin. ƒ(x, y) = ln (2x + y + 1)
- The base of a solid is the region in the first quadrant bounded by the graph of y=2x-x^2 and the x-axis. For the solid, each cross-section perpendicular to the x-axis is a square. What is the volume of the solid?The first quadrant area bounded by y2=8x, x=2 and y=0 is revolved about the x-axis. Find the centroid of the solid revolution.find the center of mass of a thin plate of constantdensity d covering the given region. The region enclosed by the parabolas y = x2 - 3 and y = -2x2
- 1. Find the area of the plane region bounded by y = x2 - 4x and y = x(2 - x) 2. A stone is thrown vertically upward from the ground with an initial velocity of 40 ft/s. How high will the stone go?A cylindrical shell has a thickness of 0.2 cm. Using differentials, approximate the volume of the cylindrical shell, in cm3, if it has a height of 40 cm and radius of 5 cm a. 60pib. 80pic. 112pi / 3d. 122piThe region between the graphs of y=x^2y=4x is rotated around the line y=16The volume of the resulting solid is