2007 sol

2007 sol - MA 165 FINAL EXAM Fall 2007 Page 1/8 10-digit...

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Unformatted text preview: MA 165 FINAL EXAM Fall 2007 Page 1/8 10-digit PUID # RECITATION INSTRUCTOR RECITATION TIME LECTURER INSTRUCTIONS 1. There are 8 different test pages (including this cover page). Make sure you have a complete test. 2. Fill in the above items in print. Also write your name at the top of pages 2—8. 3. Do any necessary work for each problem on the space provided or on the back of the pages of this test booklet. Circle your answers in this test booklet. 4. No books, notes, calculators, or any electronic devices may be used on this exam. 5. Each problem is worth 8 points. The maximum possible score is 200 points. 6. Using a #2 pencil, fill in each of the following items on your answer sheet: (a) On the top left side, write your name (last name, first name), and fill in the little circles. (b) On the bottom left side, under. SECTION, write in your division and section number and fill in the little circles. (For example, for division 9 section 1, write 0901. For example, for division 38 section 2, write 3802). (c) On the bottom, under STUDENT IDENTIFICATION NUMBER, write in your 10-digit PUID number, and fill in the little circles. (d) Using a #2 pencil, put your answers to questions 1—25 on your answer sheet by filling in the circle of the letter of your response. Double check that you have filled in the circles you intended. If more than one circle is filled in for any question, your response will be considered incorrect. Use a #2 pencil. 7. After you have finished the exam, hand in your answer sheet and your test booklet to your recitation instructor. MA 165 FINAL EXAM Fall 2007 Name:___—_ Page 2/8 1 I'm lad—2* .x—l>—2 $+2 _ —1 For x W -2) Ix'|:—’)( 13- 0 . . - —- *2 .1 H L... M: w. ..__......>‘ :4 a C x-Vz X +7— xa—k 7+9. D. 00 E. Does not exist _ 3 2. 11m 62-2: : m—y2+ .m 3 t: —00 .0 1- ’1 W2 2 ‘2. B. 1 rm ‘61-, :0 C 6—3 'X—r2+ ' D. 00 E. Does not exist 3. The domain of f(:1:) = 1n ( 7m ) is ac .__1 V >1T7< > O A. (1,00) X'l B. (0,1) “7‘ ' ' c. (—oo,U) rx‘1 CD) (1,00) and (—oo,0) E. (i, 00) and {—00, 0) 4. For What value of c will f be continuous for all ac, if 2:1:+1, forxgc f(x)= —:1:+2, forac>c go. mmhanm )Lor mu. mu: A. 0 1 Um 3L0!) : 26 +1 Kim £(x)=—C+2 13' 5 X—‘C' ) + z—x ,OA‘WI1((>O 04M; {l Ec+t:—c+2 3 at (1'3 D. 4 Fm. C = A, f E. for no value ofc '3 km. £00 $45.: 7' X—fi—é W ,3 (It!) Omni- n..me AW 4“ 3. A MA 165 FINAL EXAM Fall 2007 Name: _ Page 3/8 i_ Q1 1 *W 5 11m 38 = ’m _,___Z__~_~_ _ B. 0 :— 5'1- C. 1 X—vi D l 0—: 4—4 L'H "L2 4 2J1"? : 'm A: , E. Does not exist 'X"’1 X‘t 1 Q_ 0 6. If f(:1:)=:z:21n$, then f”(a:) = A. $+2mln$ / £(X):'Xg% + (20‘qu 17‘ +2760)" ' 3+21nsc /{ C. 3x+2lnx 3m: 1 «flag; +915")! D. 3+2xlna: ' x 7. The equation yz lnm+y = 2:1: defines y as a function of ac. Compute 3—: at (:c, y) = (1,2). '2. i- Q‘jflfl. lira): Jr 43} :2 A- 0 x 4" 0” B. 2 . _ 2 At (x)~3)’(1)2) . (1-3 2 3.22:7. _ +22 dug ‘l'cl/X D. 4 «ii :1: 2'4 :72 ® ‘2 W 8. Sand falling at the rate of 3 ft3/ min forms a conical pile whose radius is always twice the height. The rate at which the height is changing when the height is 10 feet is : .L 7- ciV - v :— 3 . V 3T”. ["2 E? ' 3 ) 2“ A. mft/mm \\//:%1T(2’}\2) I“ B. fift/min :2in 3 - 3 . all. 1» awkw’% @ 47m ft/mm M» in. 3 Wm Mo : '3 = 4“ “’0 ax D m ft/mm ‘3 %? mow E % ft/min MA 165 FINAL EXAM Fall 2007 Name: ___——_r Page 4/8 . 4 9- The funCtlon f = 37 ’ m—Z has a A. relative max at a: = 2 S’Q) : 1 + .33 B. relative min at x = 2 £1“) 0 1 + g, 3 o _,_, x =.—2 © relative max at a: = —2 = f ’5 ‘ fl ' 7‘ _D. relative min at x = —2 f (X) I "' E. none of the above 3(7’2) 3... <0 W rel-mar of 2:.»2 1 4 1 3 1 2 . . . 10. The graph of y = 13 a: -— g m + 5 a: has how many inflectlon p01nts? ® None B 1 a}? .. xZ—ax +1 = (“‘9 30 C' 2 W1 ‘" D. 3 ,H, *Jmtjw itiniwx E. 4 J, CU A11” CU 1 3‘ m lnféatlb‘fi“ ’FOIJ 3 11. The maximum slope of the curve 3/ = 6:32 — a: is A. 16 Elia: 47.x — 3x2 B. 2 “W ‘1' C. 6 ebpe'm:1‘2.y-’37i D 4 Mzigflgx \ ® M 12 elm . M T At 7-52.: “$32442- 3'2 max 12. If the highest point on the curve y = K —— x2 — 4a: is on the m—axis, then K = m :- "QIX-‘l’ : —-2éx+2) A. 0 M 4» .o —-—-.—-—- —4 fil Ar + 5’ C. —2 «fix ‘ "'7’ 6‘ may to Wmm‘ln 1 D. 1 MA 165 FINAL EXAM Fall 2007 Name: _— Page 5/8 13. A linear approximation shows that (16.2)% is approximately E670 as $629+ lt‘Mka), ylor‘ “x ma, i A. g0) -.: “2&4 (is/1e B 2+ 1 f ’6‘): EL 753/4 . 210 {06) =2 ) £067“? "277’ 32 D 2 1 . +—— £(x> (A; 2 + gig-(x,16)?Fov 7; new 16 32 H1412) m :2. +31; (162- ’15) 1 :2+-§'§(02) :2+'§5 14. Let P be the point on the curve y = fl that is closest to (5,0). The :c—coordinate of P is j (5m Lad; A. 3 D B. g 2 (5,0) “ @2 x D ~ \l(x—5)1+(V7)Z =\{ X1—30x+25+>f D. Lé—g ' \{ WW“ E. 4 D : XZ—‘bHZS &D 1.. 1: Cl. WM (2.7;...9) air 7'» \{Fx‘zfl fiat—25 OH; I y ’_ a +++ x a kMum 15. An observer 3 miles. from the launch pad watches the shuttle go straight up. He measures the angle between the horizontal and his line of sight to the shuttle. When . 7r . . . . 1 . . that angle is Z, it is increasmg at the rate of Z radians/ sec. How fast 18 the shuttle rising at that instant (in miles/ sec)? {(1119: 4h" A. 2 ‘3 h 2 Qua“ \ 5&9. 15 $2415»- ~—’ 1.1: 3 <1): 01 W 8:E . $191-1. ‘ km 4 “33;?”31 L ’1 D. 12 2- ‘fiv’2w1' S€C6~wgze 1a) MA 165 FINAL EXAM Fall 2007 Name: 1 2 1 LL w 1 16./$e$da;=..1.—( BALL-zéfi tL(€_L) 2 0 t 2 0 o 2 A. e— uZX,dAA:21<ci78 2 X10 -—P “=0 e_1 7:1 —-\-\:1 2 ' 6+1 C. 2 D. 6—2 62—1 E. 2 ,‘y I I _1LLH‘ ,smx LH , flmsa‘,_’}, l7 11m (:0st = gum : A“, "#5.... _' 2 0 '9’ B 0 o C 1 a 2 E. 2 15' 1 ’z 0- I. 18. / 1 . *1 dm_ f an» 2" Mil % \/ 1—x2 sm :1: JG]; cL C M M. - '1‘ X 4 Muflmmpvw " ‘N US $1“ 'X z: I; 11- 1113 4% {11,2}, 1 '" I B 1 2 .1], n “ii—au'gr "Q‘3c 0212 D. 1n4 E. 21113 {L t ‘ 0 3 A. 19 / xx/a:+1da:: (LL—90:441.: {’2 > :2 - aux—ix 5‘ 0 34 4 _é x :u’L _ E ” "I? B —§ “="1 —-; u: 2 2 o 4 X50 -——3 LLfr'L : a“ .2; — 4 C _5 5 3 ’ :5 3 -f% E. —% MA 165 FINAL EXAM Fall 2007 Name: Page 7/8 ( )2 X A 62 I r; 4 e B 4 :: e --"’ :-——-"""" e F (X) 25 16? @ a F__/() 64 e4 42 4 :' 1—:— -----~" D e— 217? 4- E a 21. Iff'x = 1n “3, the f’ = 1 M <. x) 2 n;Z (e2 X gnaw) gm:e““”: Be / armor”) 1 k an mi] 0 1 f(x) ': € 1 + { 1 e D 66 eQ/vl 110:2)-' {(2) :: e ( fizz '* t o E 2 = "Ham 1 " ea“) 22. The area of the region between the graph of y = 1+1m2 and the x-axis, from as 2 1 tox=\/§isr 3 “(L 3% 1r A-fw'¥v3dl>(:-tww7< A-§ ' 1 1+”X ‘1 B. % .. -1 : tam (7.2: ’tcun 1 C. q— .1r... .. I: :13; 3 4- 1 E. {-23 23. The half—life of a radioactive substance is 80 years. In how many years will its mass decrease to % of its original size? ' ' k mZMOBt A'21n80 i (“so ln2 2 m" ° 31523” B. 5111—: what-aw —+ k=—- 80 1115 «ill-Qt 0.4011— i‘. mzm e 8%) ln2 7 a amt. V D ln2 t. L", =moe 30 0mg- '40E — lnzt “92-: 1n5 _. -"‘ o — 2 @801n2 MA 165 FINAL EXAM Fall 2007 Name: —— Page 8/8 24. The focus of the parabola 11:2 + 2x — y + 3 = 0 is at X2+2x 'Zkg—B 25. The ellipse 9:132 + 41/2 — 36:13 + 83/ + 4 = O has vertices at the points (ff—3c x + +4232+Qké =4 A- (2’45) and (2%) 4B. (—2, —4) and (—2,2) 9572—” + )++@ +23): 7:53 (_2,1)and(_2,6) 9631-4” +4) + 4 (31+2‘é*’1‘)g"++ D. (—4, 2) and (2,2) gzx-zrwmwe @ <2w—4><2,2> ‘2. r "Z dig-2‘ + :l. ( cW‘er (21—1.) ' ’l‘vl 01:3 l :. V(2 Vu‘tfufl Cut (2;?) M (2/ Lg” imwmmflwpx ...
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2007 sol - MA 165 FINAL EXAM Fall 2007 Page 1/8 10-digit...

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