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Unformatted text preview: MAC 2311 AM April 3, 2009 Exam III and Key Prof. S. Hudson 1) [30 pts] Compute the derivative, y a) y = sin 1 ( x 2 ) b) y = (sin( x )) x c) sin( xy ) = y 2) [10 pts] A farmer has 200 yd of fence with which to construct 3 sides of a rectangular pen. An existing long, straight wall will be the fourth side (you can ask about a picture). What dimensions will maximize the area of the pen? 3) [10pts] Graph f ( x ) = xe x including any stationary points, inflection points or asymptotes. You can use this: lim x →∞ xe x = 0. You can use e ≈ 3 and e 2 ≈ 7 to plot points (for example instead of (1 ,e ), you can plot (1 , 3)). 4) [10 pts] Find the maximum and minimum values of f ( x ) = x 3 3 x 2 9 x + 5 on [ 2 , 4]. 5) [10 pts] Compute the limit lim x → tan 1 (2 x ) 3 x 6) [20 pts] Answer True or False. You do not have to explain. An absolute maximum must be a relative maximum. If f ( x ) > g ( x ) on (1 , 4), then f (3) f (2) > g (3) g (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.
 Spring '08
 STAFF
 Calculus, Derivative

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