Sol-166E1-S2006 - MA 166 EXAM 1 NAME GR,DlNG KEY 10—DIGIT PUIDV RECITATION INSTRUCTOR RECITATION TIME DIRECTIONS 1 Write your name 10—digit

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Unformatted text preview: MA 166 EXAM 1 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. Spring 2006 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 6 (10) (7) 2 . Credit for each problem is given in parentheses in the left . No books, notes or calculators may be used on this test. statement is always true, or F if it is not always true. atom»? two» (iii) a.(5xa=(5.g)x(5_a , twain’ affix.» 'm mm". t” (iv) 5'(E+a=5'3+5'5 always “Dru. ‘ 1* "1" “7" "' *7."_":‘* (V)(5><5)><&'=6 hfltdi-lvfufistrthl-Xg)xt:RXL—B . Find the center and radius of the sphere x2+y2+z2—2$+6z=15 hand margin. (X2+2x +L)+ '37“ +(2'z+gz+</) =15+1 +‘P (X~2)2”+ ‘31” 4426):: 25 cmtem (Lax-'3) @ vchM 5 1. Let (1', 3, 6' be three-dimensional vectors. For each statement below, circle T if the —-'2 PT; i CMLQ amt, mm ml“ ‘w /ww‘\ NYC? “6 MA 166 Exam 1 Spring 2006 Name —— Page 2/4 a —o (15) 3. If 5 '+ 23'? k and 17: 33+ 13, find the following 3 Pt” ad" b ".1‘ 1'O+2‘3+(\_—Dt 1: a .4. 1'3 -7" 7' (b){ixb: L l T: "(7‘+3)'J (1’)+k(3) O 3 1 5L " A +3k | W (c) cos0 Where 0 is the angle between ('1' andl; 3‘; £059: -— 5 M :—§--—— --——-T5:..—“ A I) Vii-4+! 9+1. 60 S y a 3 \g (d) the area of the parallelogram determined by {i and b ,j a -> é?" [uxbl =‘(Qs+1+‘9 alas I (“‘35 ’ s. 3 Q9 i a (e) a unit vector orthogonal to both {i and b —-9 1 1» '7 '9 7' " ""’ 1.1:..wa ‘1“... 5‘1— +3k _._..- 5'1. --5 +3 15 16:?be '55 (~ 3 ) r3? ( D (6) 4. Let A(1, 2) and B(2, 0) be two points in the plane. Find the coordinates (p, q) of the point C(p, q) such that AC : 2AB. XE x; 44.,—2> P73=<V°'H°).‘2> @ REL-.2373 '. <P-3;$“'z> Mar» (6’ I P-) :2 --—»:> F33 ‘ : .— 9-“2 2.4+ 9,132 (N) (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:i0 dC:_1o (b) parallel <1,C,2>X<-2./ -—l)—4~> :6 T 7*: ‘:T(—+c+'>.)—§(.4+t+)+r("*2'9 ’1 C 2. , \ _ -— a ‘ C: —9 z; _.2 _1 _4 .4C+2-G) 1+2 0 c 2 Q}: <1) c)2>4: k<'.2l-LI—4> whim: 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 y=$2 and y=$+2. ,_.‘~;l=x*2 Pat'th o; I’wrax’aad'ion: x2: x+2.-—a Mitzi—2'30 J if * (mm; = - .‘ .2 5' 2 1.’ Wxg=x Arm of WwaumaIy'M vactaw%& it. 1;, M M AA : [(x+2)—-x234>'<‘ .4. X .219 ‘1 .2, x A :§ (ma —x )flL‘x 2‘; A- L<X+2>dx_fxzolu -1 \mrwj Q) -' 2 - x3 2 (9 @ k . 5' 3;- (ZX’? ’4 Rule* 0 are.th 11m“ lovch mow, —— i item in wrap - a a .9. - 9 (two, <2 +4 3>"(J§-2*"i mm lamahfln rm —- -3. -1, -1. ..2+»4- 3 2+- 2 3 ? .. .. J. : —i 2—; = (a g; 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 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. Va tan 0/ Mai w’asldqr AV =[7T 12—- Tl’(1-'Sl‘n’x)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? _ _, 10:14. ———-» k'XBO Ila/gt.) F ,kx ,3 @( (R: E WM) A l: 1:. 30 X ‘ ‘1/7. I —1 3:4: (W (item—34' O a 7. V2 . 4,5 {bib 45 ("PH") = 1: l = 7; J/ o @ I; 1 ft-lb r“ I ‘ ® 1 /,W_‘.,.t,..i.v.__...W.,,...,..i..fi\§\ 4- ——--l (12) 10. Find /(lnm)2d$: 'x(Q/m<) _. 3x fihx)? dQ“ -:. as) We pennicxmax olM. ': Qamxyslfdm ., ‘0er f ’2.- Ixmxdx : Xflflfiaa‘, zlxlmX—J'XiAJX]: ... xflLnx) .. 2 r “12””: (in:de ducal)?!“ Ntx :- xlbhxf—rzxK/nx + 2X +C ...
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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 University-West Lafayette.

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Sol-166E1-S2006 - MA 166 EXAM 1 NAME GR,DlNG KEY 10—DIGIT PUIDV RECITATION INSTRUCTOR RECITATION TIME DIRECTIONS 1 Write your name 10—digit

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