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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.
Q. Define Period, Amplitude and Phase Shift? Ans. Period, amplitude and phase shift are used when describing a sinusoidal curve The period of a function is the smallest
two Indiana state senate candidates must decide which city to visit the day before the november election. The same four cities are available for both candidates. These cities are l
Use L''hopital''s rule since lim X-->0 1-cos(x)/1-cos(4x) is in the indeterminate form 0/0 when we apply the limt so by l''hoptital''s rule differentiate the numerator and den
Two reservoirs of equal cross sectional areas (315 m 2 ) and at equal elevations are connected by a pipe of length 20 m and cross sectional area 3 m 2 . The reservoir on the left (
Systems of Equations Revisited We require doing a quick revisit of systems of equations. Let's establish with a general system of equations. a 11 x 1 + a 12 x 2 +......
give an example of a relation R that is transitive while inverse of R is not
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Rates of Change or instantaneous rate of change ; Now we need to look at is the rate of change problem. It will turn out to be one of the most significant concepts . We will c
for what k, q.p. kx2-8x+k can be factored into real linear factors. kx2-8x+k
Class limits These are numerical values, which limits uq extended of a given class that is all the observations in a provided class are expected to fall in the interval which
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