Math_120_December_2005 (1)

Math_120_December_2005 (1) - The University of British...

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The University of British Columbia Final Examinations - December 2005 MATHEMATICS 120 CLOSED BOOK EXAMINATION Time: 2 1/2 hours Notes, calculators are not permitted. All seven questions are of equal value. 1. (a) Evaluate ). 4 cos ( 3 x xe dx d x (b) Find . 10 ) ( if ) ( x x x x f x f ± ² ³ (c) Evaluate . sin ) 3 sin( lim 2 2 3 0 x x x x ± ± 2. (a) Determine all asymptotes, local maxima and local minima, and inflection points for the curve . ) 1 ( 6 3 2 2 ± ² ³ x x x y (b) Sketch the curve in part (a). 3. A straight river 3km wide runs due east. A cable is to be laid from a point A on the south bank of the river to a point B on its north bank, 9km downstream from A . The cable is to be laid in a straight line from A to some point C on the north bank, and from there it is to be laid in a straight line along the north bank to B . If cable laid through water costs $ M per kilometre and cable laid along the bank costs $ N per kilometre with M > N , where should C be located to minimise the total cost of the
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Math_120_December_2005 (1) - The University of British...

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