ReviewTest2Spr2010

ReviewTest2Spr2010 - Study Sheet for Test 2 MAC 3473,...

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Study Sheet for Test 2 MAC 3473, Honors Calculus 2 Keesling Test on 3/3/2010 1. Solve the following differential equation using power series. Solve for the first six coefficients assuming y = a n x n n = 0 ! " . ! y = y + x 3 y (0) = 1 2. What is the volume of a torus? The torus is formed by rotating a disc in the plane around the y –axis. 3. What is the surface area of the torus formed in the above way? 4. What is the arclength of graph of f ( x ) = x 2 over the interval [0,1] ? Determine the surface area obtained by rotating the graph of f ( x ) = x 2 over the interval [0,1] around the x –axis. 5. Determine the volume and surface area obtained by rotating the following figure around the x –axis. 6. Determine the centroid of the area under the curve. (a) f ( x ) = x 3 over the interval [0,1] . (b) f ( x ) = ! x 2 over the interval [0,1] . b a 2 a b x ! axis y ! axis y ! axis x ! axis
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7. Determine the position y ( t ) of the particle at time t given the following information. The particle has an initial vertical velocity v 0 at time t = 0 . The only force acting on the particle is gravity.
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This note was uploaded on 07/14/2011 for the course MAC 3473 taught by Professor Block during the Spring '08 term at University of Florida.

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ReviewTest2Spr2010 - Study Sheet for Test 2 MAC 3473,...

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