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Unformatted text preview: MATH 251, Summer 2007
RAICII 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.
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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
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Z 4. (10 pts) Calculate the double Riemann sum of f (33,31) 2 my + 33/2 for the partition ofR =
{(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
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m 2
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m). 251128
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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=\2x8 CJW =§£~m= Z \Zx—K: 0 gm: mm = Lima: \\ _ x: 2:3 =4 2!. L WW 6 Haz— m an) V v4 :3l§+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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 Spring '08
 Skrypka

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