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# ef04k - MAC 2312 Final Exam Prof S Hudson 1(10pts For each...

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August 12, 2004 Final Exam Prof. S. Hudson 1) (10pts) For each series, answer either Converges absolutely (CA) or Con- verges conditionally (CC) or Diverges (D). State which “test” you are using and show work. a) k =1 ( - 1) k (1 + k ) - 2 ln( k ) b) k =1 ( - 1) k 2 k +3 2) (5pts) Set up and simplify the integral with which you would ﬁnd the length of the curve y = 1 3 ( x 2 +2) 3 / 2 from x = 0 to x = 3. Do not evaluate. 3) (5pts) Express 1 - 2 / 3 + 4 / 5 - 8 / 7 + 16 / 9 in sigma notation. 4) [5 pts each] Compute (or explain why no answer exists): R tan 2 x sec 2 x dx R x 2 e x dx R π 0 | cos( x ) | dx = R + e dx x ln x 5) (15pts) a) Sketch the rose r = sin 2 θ . b) Write down, but do not evaluate, an integral for the area of region enclosed by the rose. c) Use parametric equations to ﬁnd dy/dx for this curve. 6) (10pts) a) Find the Taylor Series for the function f ( x ) = sin( x ) x at x = 0. b) Use the result in (a) to approximate the integral

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ef04k - MAC 2312 Final Exam Prof S Hudson 1(10pts For each...

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