ReviewTest1Spr08 - MAC 3473 Honors Calculus 2 Keesling...

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MAC 3473 Honors Calculus 2 Keesling Review Test #1 Test Date 2/4/08 1. Find the surface area and the volume of the torus which is formed by rotating about the y –axis a disk of radius b whose center is located at the point ( a ,0) . Find these using Pappus’ Theorem. Write down the integrals representing these. b a 2. Determine the centroid of the arc, y = R 2 ! x 2 for ! R " x " R and for 0 ! x ! R . 3. Find the arclength of the segment of the parabola, y = x 2 , 0 ! x ! a . Also find the centroid of this arc. 4. Find the area between the curves for the following pair of functions. Find the volume obtained by rotating this area about the x –axis. About the y –axis. f ( x ) = x 3 f ( x ) = x 4 5. Find the area between the curves in the first quadrant of the plane. f ( x ) = ! x 2 g ( x ) = 1 ! x 2 6. Find the volume determined by rotating the area bounded by the curves below around the x –axis. y = x 2 y = 0 x = 1 7. Show that x n n = 0 ! " = 1 1 # x for all x with x < 1 . 8. Find the volume of a solid ball of radius r .
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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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ReviewTest1Spr08 - MAC 3473 Honors Calculus 2 Keesling...

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