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Volumes of Solids of Revolution / Method of Rings
In this section we will begin looking at the volume of solid of revolution. We have to first describe just what a solid of revolution is. To get a solid of revolution we begin with a function, y = f (x ) , on an interval [a,b].
Then we rotate this curve around a given axis to get the surface of the solid of revolution. For discussion let's rotate the curve around the x-axis, although it could be any vertical or horizontal axis. Carrying out this for the curve above gives the given three dimensional region.
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Partial Fractions - Integration techniques In this part we are going to take a look at integrals of rational expressions of polynomials and again let's start this section out w
Unit Vector and Zero Vectors Unit Vector Any vector along with magnitude of 1, that is || u → || = 1, is called a unit vector. Zero Vectors The vector w → = (
a) Let V = f1, 2, :::, 7g and define R on V by xRy iff x - y is a multiple of 3. You should know by now that R is an equivalence relation on V . Suppose that this is so. Explain t
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To find out the perimeter of a triangular region, what formula would you use? The perimeter of a triangle is length of surface a plus length of side b plus length of side c.
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A cable is attached to a pole 24 ft above ground and fastened to a stake 10 ft from the base of the pole. In sequence to remain the pole perpendicular to the ground, how long is th
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