Sol-166E1-S2008

Sol-166E1-S2008 - MA 166 EXAM 1 Spring 2008 ' Page 1/4 NAME...

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Unformatted text preview: MA 166 EXAM 1 Spring 2008 ' Page 1/4 NAME -GRADI‘NG KEY 10—DIGIT PUID RECITATION INSTRUCTOR RECITATION TIME DIRECTIONS 1. Write your name, 10—digit PUID, recitation instructor’s name and recitation time in the space provided above. Also write your name at the top of pages 2, 3, and 4. 2. The test has four (4) pages, including this one. 3. Write your answers in the boxes provided. 4. You must show sufficient work to justify all answers unless otherwise stated in the problem. Correct answers with inconsistent work may not be given credit. 5. Credit for each problem is given in parentheses in the left hand margin. 6. No books, notes or calculators may be used on this test. (10) 1. Let (i, Ii, 8 be three—dimensional vectors. For each statement below, circle T if the statement is always true, or F if it is not always true. L 2 m; F“ @ F (1) (2d) - (33) = 661’- 13' (u) (6 (7)6: (ii-cw T (F) (m) (ca—5) (6+5)=l&‘|2—|5|2 _, a d, - (9 F (N) ax(5xé‘)=(dx3)xé’ Tx(l’x7)=:xfi‘:; AWOXJ’3xflz3 T Q?) (v) If (‘1' x I; 2—6 then 65 and are parallel ® F (4) 2. If 6 :2 2'? — ;+ 21;, find a unit vector in the direction opposite to it. MK la] = V4+1+4 "-713 =3 ,%(2L {15+ ‘27:) (4) 3. Find Ei- gif Id] : 12, = 15 and the angle between (i and 5is Zr— radians. —-v- a at. k =|6{HT5|0056 212.45 cos—TE 212.15%": 6 G 2 4 ~_ .1 .t t... :«ma E1 MA 166 Exam 1 Spring 2008 Name —_ Page 2/4 (6) 4. Find the values of t for which the vectors (3t, —t, —3) and (—1,t2, —4t) are orthogonal. “Bf—t3+12t=0 t_ 9 Wm .5 try-19):!) .e.‘ (4) 5. A constant force F = 33+ 55+ 10]; moves an object along the line segment from (1, 0,2) to (5, 3, 8). Find the work done if the distance is measured in meters and the force in newtons. .._.. Disf vmltor D:4?+3—§+GI © ('3 m :1 n2+13+eo H —a -—o (6) 6. Find the area of the parallelogram determined by the vectors ('1' = i+ 53—" + k and b = —27?+ 5" + 3k. imam-I” _, —-' Area. a} W/ ,72‘axbl a m. __, d a axE’: 651?? =14iv-5' +11k 5L 3 1 J @ —2 1 '5 1‘ @ vale mnss’sha‘HY V © ‘5: X 1:]: H" +(—s)1+.[11)‘ , 3 2 ._.. W + 25 .; r542 “- L91 (8) 7. Find the center and radius of the sphere m2+y2+z2+2m—10y=—1. 7- 2 X +2x +3, ~10uh +2," ;,1 Z gnu—- X +2x +1 + Kat-LIOZS-i—ZE +2.7:a'l-k1-r2b (X +1)? +63 - 5f + 21:. 25 MA 166 Exam 1 Spring 2008 Name _______—___.______ Page 3/4 (10) 8. The region bounded by the curves at = 3/2 + 1, y = —1, y z 1, and a: = 0 is rotated aboblét the y—axis. Find the volume of the resulting solid. Volumuz. 0/ fifFYoximat/"a disk 2 2. @ AV:TF<\3 +1) A} Rule. *2 0,213 fovmble I '2 X:"3+1 -1 w“ "1 G) {ll movgflnqm1c‘l‘3m k}, 1 + (D 5 _ Wrong: Limit» coun‘tnn \1 ‘2 $0 +2.32;— 1. Rim 1". 5‘ '3 1 2. ='2"‘[——-—2- +%-g+al=2w[é+§+1l 56,,- O =Q1T 3,210+15’ = 15 © ’0 (10) 9. Find the volume of the following solid 8’ : The base of S is a circular disk with radius 7‘. Parallel cross—sections perpendicular to the base are squares. '3 l???” Talk éimFmallfl Cr¢ss~Mc17'4ng ".sz’Fandlhufimv P {l {0 “v. *‘OsYltf . AYQQ of cvossvfcd'l'a" GI X A09 :(2 W)“ \Io‘um 0/ $110. ‘. AV: 4 onyx-l] Ay ’ 4- v .11) ‘ zgjv(v2v_x1)i,x a a) “ p is v 2 g [ex @1232an 5;): £33 E9 (8) 10. Set up, but do not evaluate, an integral for the volume of the solid obtained by rotating the region bounded by the curves :1: = sing with 0 g y 3 7r, and a: = 0, about the Volum/L 0,1 3% AV '— 2TT(4"3)W 4? MA 166 Exam 1 Spring 2008 Name __—__ Page 4/4 (8) 11. Set up, but do not evaluate, an integral for the volume of the solid obtained by rotating the region bounded by the curves y = x2 + 1, y = 9 — 902 about the line 3; = —1. xiflri z 6],)”. “'1 2x‘:§+><"“=4.s“a 5 1‘ ‘E vow-M t72 LAP‘M‘ i’arlum a 2 A V -== [m«(9.x‘%é@_3(x1fkgfdbthx iiaww (6) 12. The natural length of a springis 1m and a force of ION is required to hold the spring stretched to a total length of 2m. How much work is done in stretching the spring from its natural length to a length of 1.5m? szx “aloe-k1 -—>’k=10® 0.5‘ I .L '2. 9. 5' N: imam = Ex 10:“ 0 4 W = 5,. J g (16) 13. Evaluate the integrals. .... Ml“ (a)ftan‘1xdx /'7< tam“x ~13; 1 M + may,» elvde -1 AMA—ax rum x"+1 ...
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This note was uploaded on 09/14/2011 for the course MATH 166 taught by Professor Staff during the Spring '10 term at Purdue.

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Sol-166E1-S2008 - MA 166 EXAM 1 Spring 2008 ' Page 1/4 NAME...

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