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e306fk - MAC 2311 Exam III and Key Prof S Hudson 1(15 pts...

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Unformatted text preview: MAC 2311 November 22, 2006 Exam III and Key Prof. S. Hudson 1) (15 pts) Use the info provided to analyze and graph the function f ( x ) = x 2- 2 x +4 x- 2 . [Draw the f and f 00 lines and discuss intervals. Find all the HA’s, VA’s, critical points and inflection points - if they exist]. Given: f ( x ) = x ( x- 4) ( x- 2) 2 and f 00 ( x ) = 8 ( x- 2) 3 . Also, notice that x 2- 2 x + 4 > 0 for all x . 2) (15 pts) Water is pouring into a conical tank at the rate of 8 cubic feet per minute. If the height of the tank is 12 feet and the radius of the circular opening (at the top) is 6 feet, how fast is the water level rising when the water is 4 feet deep? Hint: V = πr 2 h/ 3. 3) (15pts) Compute the limits: a) lim x → π sin( x ) π- x b) lim x → 1 + ( x x- 1- 1 ln x ) c) lim x → (cos x ) 1 /x 4) (10pts) State and prove Rolle’s Theorem (prove Cases 1 and 3 carefully, if not Case 2)....
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This note was uploaded on 05/28/2011 for the course MAC 2311 taught by Professor Staff during the Spring '08 term at FIU.

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e306fk - MAC 2311 Exam III and Key Prof S Hudson 1(15 pts...

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