F05 1205 final W - Name ID MATH 1205 FINAL Fall 2005 CRN or...

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Name: MATH 1205 FINAL Fall, 2005 ID # CRN or class time Free Response Questions CALCULATORS MAY BE USED (50 pts total) You must SHOW ALL WORK and use methods learned in class to receive full credit. Read the Directions . 1. A rectangular box with an open top is to be made using 726 in 2 of cardboard. The box has length, l , height, h , and width, w , where h equals w (see figure below). Find the dimensions (width, length, and height) that maximize the volume of the box. Show work to demonstrate that the dimensions you give actually do yield a box with absolute maximum volume. (8 pts) l w h = w 2. (7 pts) Use the graph to find the following. If the limit does not exist, give a reason . a) lim x !" 1 f ( x ) = b) lim x " 3 f ( x ) = c) Name the x values where f ( x ) is discontinuous
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3. Gravel is being dumped from a conveyor belt at a rate of 35 ft 3 /min and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 10 ft high? (8 pts) Include a labeled diagram. Recall the volume of a cone:
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