e203k - MAC 2311 Exam II and KEY July 22, 2003 Prof. S....

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MAC 2311 July 22, 2003 Exam II and KEY Prof. S. Hudson This was an 80 minute Exam. 1) [40 pts] Compute the derivative, f 0 ( x ) (shortcuts are OK, but show all work); a) f ( x ) = sin( x 3 ) b) f ( x ) = 1 (2 x +1) 3 c) f ( x ) = x +1 x d) f ( x ) = ln(ln( x )) e) f ( x ) = x x f) f ( x ) = x 2 sin( x + 1) g) f ( x ) = csc(2 x ) h) f ( x ) = x 3 + 1 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] A gas balloon is being filled at a rate of 100 π cm 3 of gas per second. At what rate is the radius of the balloon increasing when its radius is 10cm? 4) [10 pts] Find the maximum and minimum values of f ( x ) = x 3 - 3 x 2 - 9 x +5 on [ - 2 , 4]. 5) [15 pts] Answer True or False. You do not have to explain. The derivative of a product (
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e203k - MAC 2311 Exam II and KEY July 22, 2003 Prof. S....

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