001 Math 149 002 Exam 2 Name I Pal e 1 of 5 circle one Dr P D McCra 28 March 2006 1 20points A page of a book is to contain 27 square inches of print If the margins at the top bottom and right hand side are to be two inches and the left margin to be one inch find the dimensions of the page which uses the least amount of paper a Draw and label an illustrative diagram b Write one or more equations expressing the relationships between the quantities c Express the unknown quantity to be optimized as a function of one variable d Use the techniques of calculus to complete the solution of the problem I I kJ i t If 5 fj H i X I 1 1 L oj A It If Wh B II f IV 3 1 7 t4 I 3 f I J I If X 2 I y 2 1 I 2 1 1 T b l T JT f 3 X L d w 1 X 3 7 J 1 4 CO I f c I X J 7 C 3 Lf I 7 V 0 3 z z f 3 2 f b4 z z Po 3 f rXJ T l f l 2 j z 1 K 3 3 trY1 4 7 2 3 f I r 1t 1 3 2 Z 1 1 3I2 It 0 o W L J X IE Math 149 001 002 Exam 2 Name circle one J 28 March 2006 Dr P D McCray 2 20points Find dy if dx a x3 y3 3XY J e it VYI 3f q tr 3 3X i 3i 3 J2 rx 4 x l 3 3X2 X2 2 lic 2 b xsin y ysin x I X 1 I t CU 1 t1 d x j k 0 1 l tPx f1 CP JX tJ J r Math 149 001 002 Exam 2 Name circle one Dr P D McCra 2arctan 3x f I K1 I I 3X 3 K I C c 10 points hex 4arccos 5x 4 I arctan 2x3 1 7 I i X 2 x 5 3x2f I of 4 I I 11 I X2 1 y t X 2 I 1 Pasze 3 of 5 b 5points g x 28 March 2006 3 20points Find the derivatives of the following functions a 5points I x l l t Math 149 001 002 Exam 2 Name circle one Dr P D McCra A 28 March 2006 IE Page 4 of5 4 10points Find the most general antiderivatives of the following functions a I x 4 1 x2 4 f F JC 4 6 r x J fkv J L I c h fX I R e C G I tK d fx 5 lOpoints Find h x if h x sinx cosx I J h O l and h X J CI 0 C h IXJ O 0 CI h r IC Y X I O I O 7 l K C Jf h fi f CP f f C L 2 J 7 J C z Z Z r r z z 7 rz 2 z Z C Math 149 001 002 Exam 2 circle one Dr P D McCra 28 March 2006 5 20points A car is traveling at 45 mph that is 66 feet second On dry pavement with tires in good condition when the brakes are fully applied the car is capable of producing a constant deceleration of 22 ft s2 a How long does it take the car to come to a stop when the brakes are fully applied b How far does the car travel from the time the brakes are applied to the time the car comes to a full stop a 1 1 v 6 z z D t v f b 2 2 t c vI 0 2 Z S b 0 b1 C1 2 2 E 2 2 51 1 C II t t Z S f t i kM t f V f s I 0 654 S 3 b 2 2 6siDp 2 z 3 1 L z be 3 11 f Itf 99 qq SJ k
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