MATH
Team Homework 3.docx

The height of a shell will be 1 because this is the

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axis and we subtract this distance from 1 to account for the center tower. The height of a shell will be 1 because this is the difference between the top of the tower (which is bounded by the function given) and the bottom of the tower. This gives us volume= 1 2 2 π ( x 1 ) 1 . The limits of integration are 1 and 2 because the region which creates the tower is bounded by x=1 and x=2. This integral is improper because the function blows up at x=1 so we must replace the
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lower bound and rewrite it as a→ 1 + ¿ a 2 2 π ( x 1 ) lim ¿ ¿ . We can then evaluate the integral using u- substitution and find that the volume is 4 π 3 m 3 . B. Print.juice would eventually go bankrupt because although the amount of plastic required to create the tower is finite, the central column of the tower will have an infinite volume. The amount of plastic required to create the tower is only dependent on the region given to us and this region has a finite volume. The empty central column however will go on forever and therefore have an infinite volume.
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  • Fall '07
  • Irena
  • lim, #, 3 M, LCT, 116 Sec

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