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1205finalF2006 - Name ID MATH 1205 CRN FINAL Fall 2006(50...

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Name: MATH 1205 FINAL Fall, 2006 ID #: CRN: (50 pts total) Free Response Questions Read the Directions. CALCULATORS MAY BE USED You must SHOW ALL WORK and use methods learned in class to receive full credit. 1. (8 pts) A manufacturer wishes to minimize the cost of materials to produce 1 liter (=1000 cm^3) cans (cylindrical). Assuming the thicknesses of the ends and the side are the same, what is the ratio of the height to the diameter of the can that minimizes cost? 2. (7 pts) Given f ( x ) = ! 4( x 2 ! x ! 2) x 2 ! 5 x + 6 . Evaluate the following limits. State + ! or " ! where appropriate. a) lim x ! " 2 f ( x ) b) lim x ! 3 " f ( x )
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3. (12 pts) Find dy dx of each of the following functions. Simplify your answers. a) y = tan ! 1 ( x 2 ) ( x 4 + 1) b) y = ln 4 (sin(3 x )) c) 2 x 4 y 3 ! 8 x = y 4. (8 pts) A police cruiser, approaching a right-angled intersection from the north, is chasing a speeding car that has turned the corner and is now moving straight east. When the cruiser is 0.6 mi north of the intersection and the car is 0.8 mi to the east, the police determine with radar that the distance between
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