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Sol-166E1-S2006 - MA 166 EXAM 1 Spring 2006 NAME GR,DlNG...

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Unformatted text preview: MA 166 EXAM 1 Spring 2006 NAME GR ,DlNG KEY 10—DIGIT PUIDV 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 3 . The test has four (4) pages, including this one. . 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. . Credit for each problem is given in parentheses in the left hand margin. 5 6 . No books, notes or calculators may be used on this test. (10) 1. Let (1', 3, 6' be three-dimensional vectors. For each statement below, circle T if the (7) 2 statement is always true, or F if it is not always true. (i) 5-5235 alum); tw .—- 2: (iii) a-(Exa=(a.5)x(a-a not tax. 3-}: Mm) Kiow- . s, . . , (iv) 63-(5+é’)=é'~3+&'-€ always t‘er... (V) (5X5) X5=6 not d-lW&~3,§ limp. U x 5):: . Find the center and radius of the sphere x2+y2+z2—2$+6z=15 i: 14.x (X2+2x +L)+ '37“ +(2'z+gz+</) =15+1 +‘P LX~))2’+ if +(Z+'5)2: 25 cmtem (Lax-'3) @ vacuum 5 ® —-'2 PT; £11 CMLQ mm. mg ml“ .w /..__._,.\ NYC? “6 MA 166 Exam 1 Spring 2006 Name —— Page 2/4 (15) 3. If a ) 2+ 2;_ nd 1—; : 3i+ 1;, find the following 3 P5) {ALL (3 13’ #a :1'0 +- 2‘3+(:D1 ‘3’" 5 m “1 (b) Ez’xb : T '3" T: =1(7**'3)‘3 (1-) +143) W‘s} (c) cos0 where 0 is the angleS between ('1' and b E ‘3 C059: m 01-? .1, 3.2:..- ”fig-3 '3 A l mug}: V1.31”! 9+1. “‘55 “’0 S y a 3 \g (55 (d) the area of the parallelogram determined by {1’ and b ,j 3—». -> ‘é‘?’ f; [uxbl 27135331339 2:135" I ("353 ’ 1. 3 .3 Q9 '3 l. (e) a unit vector orthogonal to both a and b d, 0.21% a . -" —-§ uxwwmw‘: 5 _ 3k .34.. 5' -5433 - s lam “1‘3"3(‘ 1* )333( l '3 (6) 4. Let A(1, 2) and B(2, 0) be two points in the plane. Find the coordinates (p, q) of the point C(p, q) such that AC— — 2AB. AB :3. <¢,— > Ac=<xs—L,ey2> .3 .... (3) AC: 2MB '. 413-533;?» mag—34> (G) \( ::;:2_4 ~-3::"5’2 ‘ (103(1): ('3’ -2) E1 (8) 5. Find the value of the number 0 such that the vectors (1, c, 2) and {—2, —1, —4) are (a) orthogonal <1, C,2>‘<‘2,’1,“l> '20 -2’C-‘E:;0 ”szio (b) parallel <1,C,2>X<-2./ -—l)—4~> :6 T T 7*: ‘:T(—+c+'>.)—§(.4+qr)+r("*2'9 ’1 C 2. 3 \ _ 3— a ‘ C: —9 z; _.2 _1 _4 .4C32-G) 1+2 0 c 2 Q}: <1) C)2>3: k<"l,"1.’-4> gulp-3.11M k in anflw '2. -l. MA 166 Exam 1 Spring 2006 Name __ Page 3/4 (10) 6. Find the area of the region enclosed by the curves 312519 and y=$+2. ”424”“? $30in 0; .Mrvmi'ion: x2: x+2.-—a glam-"2'30 “I J (,1 * (x—amw) = - .‘ .2 5' ’1) 2 1.’ Wxg=x Arm of Difimi WwaumaIy'M vactaw%& it. 1;, 1... M AA : [(x+2)—-x234>'<‘ .4. X .219 ‘1 .2, x A :§ (“—2 —x )flL‘x 2: A— L<X+2>dx_fxzolu -1 \mrwj Q) -' 2 - x3 2 (9 @ k . 5' 3;- 2x"? ’4 Rule* 0 credit 11m“ ‘0?ch {A mow, —— W i item in Wrcr - . _, fl. - 9 (two, <2 +4 ”37>"(J5-2'Hi mm lamahfln rm —- -3. -1, -1. ..2+»4- 3 2+- 2 3 ? .. .. J. : —i 2—; = ‘8 if); 2. 5 2 2 @ (16) 7. Set up, but do not evaluate, an integral for the volume V of the solid obtained by rotating the region bounded by the curves 3; 2 51:4, 31 = 0, and a; = 1, about the sv—axis, (a) using the method of disks /washers ('1’) Volumme all Wheat} 9051(0- A V : “(x 4) A7: , MA 166 Exam 1 _ Spring 2006 Name _— Page 4/4 (8) 8. Using the method of disks/ washers, set up, but do not evaluate, an integral for the volume V of the solid obtained by rotating the region bounded by the curves 3; = 0, y = sinm, 0 g a: 3 7r about the line 3; = 1. Votlxme 0/ talommi w’ashm AV {7112- 1r(1-Sinx)2j4x (8) 9. A force of 10 lb. is required to hold a spring stretched 4 in. beyond its natural length. How much-work is done in stretching it from its natural length to 6 in. beyond its natural length? szx —» 40=l< ’1 ""9 {-33.0 (lb/gt) F—sox 3 @ (‘E'V‘Q i/ - a... W=J7§>0xeix '1M‘imwfi Ln, t}: ft. W1 gauh43 I 4‘: (tn-41>) -:: 13le/1 :7 32' it’ll” & o G») 5" ~12“ ES 0 /--.---.--. 0.....---.--...N (12) 10 Find /(lngr:)2 dm: (Wrng) 3X Bum?!) Ba pawl» :l’lmX) ch: «3% 0‘“ - 2am $32611 . ru:x X(anx)1.2£lmxclx =xfhtx) ZLX‘Q/“X— ~JX 2610‘]: dim-44X (Vt X :- xfllmx) —2xK/nx + 2X +C ...
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