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# ef07fk - MAC 2312 Final Exam and Key Prof S Hudson 1(10pts...

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MAC 2312 Dec 11, 2007 Final Exam and Key Prof. S. Hudson 1) (10pts) For each series, answer either Converges absolutely (CA) or Converges condi- tionally (CC) or Diverges (D). State which “test” you are using, and show your work. a) k =1 cos( k ) /k 2 b) k =1 1 k ln k 2) (9pts) A cylindrical water tank of radius 5 ft and height 9 ft is two-thirds ﬁlled with water [density = 62 lbs/ft 3 ]. Find the work required to pump all the water over the upper rim. 3) [5 pts each] Compute (or explain why no answer exists): R e 1 ln( x ) dx R cos 3 x sin 2 x dx R 2 x dx R 2 π 0 | sin( x ) | dx = R + -∞ 1 x 2 +2 x +5 dx 4) (5pts) Write down, but do not evaluate, an integral for the area of region enclosed by the rose r = sin(3 θ ). 5) (10pts) Let x = t and y = 2 t + 4. a) Find dy/dx when t = 1, without eliminating the parameter. b) For the same curve, ﬁnd d 2 y/dx 2 when t = 1, without eliminating the parameter. 6) (15pts) a) Find the McLaurin Series for the function

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ef07fk - MAC 2312 Final Exam and Key Prof S Hudson 1(10pts...

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