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251S07_2A(Green) - MATH 251 Summer 2007 RAICI-I EXAM 2...

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Unformatted text preview: MATH 251, Summer 2007 RAICI-I EXAM 2 - VERSION A Name (printed): GMEEN KEY Section #: “On my honor, as an Aggie, I have neither given nor received unauthorized aid on this academic work.” 1 Signature: UIN: DIRECTIONS: 1. The use of a calculator, laptop or computer is prohibited. 2. Please present your solutions in the space provided. Show all your work neatly and concisely and clearly indicate your final answer. You will be graded not merely on the final answer, but also on the quality and correctness of the work leading up to it. 3. There are questions on BOTH SIDES of the paper. Please be aware of this. DO NOT WRITE BELOW! Question Points Awarded Points 1Disputes about grades on this quiz must be 'handled the day the quiz is handed back and must be discussed before you leave the room. If the quiz leaves the room, it will not be re—evaluated (except for possible adding mistakes). 1. (10 pts) Carefully sketch the curve of the polar equation 7' : 0, 0 _>_ 0. . v- 3:! 3Q)! mi fig ' +73 (fit Kim 3 9 2. (10 pts) Reverse the order of integration of f / ex” dy dm. DO NOT EVALUATE. 0 :52 0 1/4—y2 3. (10 pts) Convert the following integral to polar coordinates: / / (m2 + y?)3/2 d3: dy. DO —2 0 NOT EVALUATE. ' x= '+1 o 1 Kill/2:: S l (3 rolrdlé) J; 0 Z 4. (10 pts) Calculate the double Riemann sum of f (33,31) 2 my + 33/2 for the partition of-R = {(3:,y) : —1 S as S 2, 1 S y S 3} with partition lines a: = 0 and y : 2 Where~(m;*j,y;*j) :’lower left corner of jo. i ifixmmw 5. (20 pts) Use a double integral to find the area of one loop of the rose curve r : 2sin(20). § r o" o m 2 “I; o “\1 Qémze 8 WM) Jr \1 O 0 > m). 251128 ‘3 37f (Jae U o 6. (20 pts) Find the absolute maximum and minimum values of f (w,y) : 3:2 + 2mg + 33;2 on the closed triangular region with vertices (—1,1), (2,1), and (—1,—2). ' ’g WW = XZ‘ererBx/Z -§ OLU \W 1 <2>< -\—le\ 2x+6v> X“‘\/ X: -3\/ QLCMfi: _ M \fx: .4 e x21 Vi -\ 5x97. \Lbd = “X OH) = XZQbe) +3 be? \Lmz x2+2x2— 2x (3)82 éy +3 JV"\ \LM: @5— 8>< +3 @[XWszW = x32x+3 3M1 (M031 Ur. , 2‘ f 9* 0H ( \L‘M=\2x-8 CJW =§£~m= Z \Zx—K: 0 gm: mm = Lima: \\ _ x: 2:3 =4 2!. L WW 6 Haz— m an) V v4 :3-l§+i:‘l3 \AH 44~\o,\<\-2+31 a 75 g V \/ V \<(—\\= H4 1): WM: (NJ AVA ‘ \Lm 5%? \\ \ \\ abs my $7 on HQ) 0% mm 0 m (0,03 kl 7. (20 pts) Find the center of mass of the lamina that is the rectangle [0,2] x [0,1] if p(m, y) = 32:2 + 2y. ' : dim, M M _ 30 SBXLZXV My -megaasw 1%va W +10 My 8 {M W 0h 0‘? =\;\1+L\w¥j : S x v +RXY1C0‘V : \§:2i\lb% {fix/“WW AVE m—\=K% [£33 LEO—7% “WW; : ' ...
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