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Unformatted text preview: MAC 2311 Dec 12, 2005 Final Exam A [recent topics] and Key Prof. S. Hudson 1) (20 pts) Compute and simplify; R x 7 + e x dx = R sec( x ) tan( x ) dx = R 2 x x 2 +1 dx = R 1 2 t 3 t 3 dt = 2) (15 pts) More: R e 5 x dx = R cos 2 ( x ) dx = R tan 2 ( x ) dx = 3) (15 pts) A rancher has 200 feet of fencing with which to enclose two adjacent rectangular corrals (I drew a picture on the board  imagine a rectangle divided down the middle by a vertical line). What dimensions should be used so that the enclosed area will be a maximum? [If you dont understand this story, ask me!] 4) (15 pts) Sketch a graph of y = x 2 1 x 3 . Find all critical points, inflection points and asymptotes [and label them clearly]. You may use: y = 3 x 2 x 4 y 00 = 2( x 2 6) x 5 3 1 . 8 6 2 . 4 1 . 8 3 . 18 2 . 4 3 . 07 5) (10 pts) CHOOSE ONE; A) State and prove Rolles thm. B) Prove that if f ( x ) &gt; 0 on [a,b] then f is increasing on [a,b]....
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 Spring '08
 STAFF
 Calculus

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