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Unformatted text preview: MAC 2311 November 21, 2005 Exam III Prof. S. Hudson 1) (15 pts) Use the info in these number lines [which were a bit clearer on the real exam] to describe the intervals of inc/dec and concavity for the function f ( x ) = e- x 2 / 2 + + + + + + + + + + + + (0)- - - - - - - - - - - - - f + + + + + + (- 1)- - - - - - (+1) + + + + + + f 00 2) (15 pts) Analyze and graph y = x 4 + 2 x 3- 1. Plot and label any critical points and inflection points. 3) (10pts) Use both the First and Second Derivative Tests to show that 3 x 2- 6 x + 1 has a relative minimum at x = 1. 4) (15pts) Compute the limits: a) lim x → π sin( x ) π- x b) lim x → csc( x )- 1 /x c) lim x →∞ (1- 3 /x ) x 5) (15 pts) Mark each sentence True or False; sec( x ) has a maximum value on the interval (- π/ 2 , π/ 2). sec( x ) has a maximum value on the interval ( π/ 2 , 3 π/ 2). If c is a critical point of f , then f has a relative extrema at c ....
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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.
- Spring '08