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2005 sol - MA 165 FINAL EXAM Fall 2005 Page 1/8 NAME 50...

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Unformatted text preview: MA 165 FINAL EXAM Fall 2005 Page 1/8 NAME 50 LUT\ON$ 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 2005 Name: ___—_ Page 2/8 1‘ $133512 it: : £1312 :ff; 2 ’1 ® ‘1 ' B C D le =-7< W x=—‘2 E. Does not exist m—)2+ . 0 9m '5 we @ \ ’UM f € 2"" = 0 C 6‘3 x—sZ D. 00 E. Does not exist 53—1 3..— >0 A (1,00) X—L . 0.1 15L W 1: (')0 x _ _ X'l 0 1- (m?) (17 00) and (—00, 0) E. (i, 00) and (—00, 0) 4. Find the value of c for which the function 2-’E + 1, if :E g c flat) = { , ~5E + 2, 1f :3 > c is continuous for all at. 1 ‘ e in mvfipmm for all X $C (Polymmlah M CDJ‘V‘MELS) A. 0 {(c) s ‘Zc +1 1 . B. _ 9mm £09 =— 2c+i QJm 9x) : —C+2 2 x—ac' x.» c" 1 14m £60 exist, 3} 2c+l = —c.+2 © '3; K—ac __I or Cv'é' D 1 WM C=j§ . 4 : {6;} mol 3“”th ”til; E. fornovalueofc f‘ § 3:” u WM MA 165 FINAL EXAM Fall 2005 Name: —— Page 3/8 a I I . cos — 1 Ll+ . ___. ' L” _, 5- 11m ——$ = L171 Jill-2‘— —- if," («OSX $6.0 ”32 X-do 2x xeo 2 A. —11 '9' 3— .. _ i ® 7 0 a - E C. 0 D. 1 E. Does not exist 6. If f(:i:) = 3321113; then f”(a:) = A. $+2$ln$ I £(X): X23:— + ZXLhX :x+2x1my .3+2lna: Y // 'A C. 3$+2ln$ {a} ’ 1 + 2, 3‘ + 2'1”“ D. 3+2xlna: :3 +2“): E. l a: . , d 7. The equation y2 lna: + y : 23: defines y as a function of 3:. Compute d—y at :1: (33,31): (1,2). gzéi—Qaéfl-me-kfi'sz A.0 ob< B 2 At (whlkz) 1 ' 2 . .t+e=2 0: 4+22£§E§ A“ D'_4 dm 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 fl:3 \J =‘LVV2L #:2l‘ A. —3 ft/min ‘3" . - 1 3 and 2%. Wm we 400” V:§W(2\n) h OUT B ift/min 3 2007f V =%_fl‘ln 3 vy— : 4-th .413- © —4007r ft/mln M dX Wm M=Ioz “3:417 10" :1 D fift/min (Mn _ '3 t 1 Era:- '35:... {7/th E aft/H1111 MA 165 FINAL EXAM Fall 2005 Name: 9. The function f(a:) = a: — i2 has a a: I g (x): 1 + 33;; I '5 . ' §(*):0 '. X:_8—ax—,--2 // _. __ 24 5' (x) , ._2; 16 g [Arm ”km, a1 x:'2 Page 4/8 A. relative max at a: = 2 B. relative min at a: = 2 © relative max at a: = —2 D. relative min at a: : —2 E. none of the above 1 10. The graph ofy: 53:4— %a:3+%a:2 has how many inflection points? Chg I 3 '2. .None Ti? 3 ‘3‘ x *x +X 13-1 2 '2 C 2 (Li. = {:21 +1 :(x-i) 30 M1, D. 3 g” t—+++D+++-+ E4 (>0 —————-—-——-—r—-————-'——">x cu 4 CU 11. The maximum slope of the curvey:6a:2—a:3 is A. 16 1.. % : va -3x B. 2 '7- C. 6 stave. S:x2x_3x ”ii _—. Wax a 12 43-8—30 L X:2; @ A): . J cL$ ++++O -—— .3Smmfl4 x;=‘2 1 .——-—‘ -————-————r—-—'-—""“? dx' 2 * S(2)=|2..2-3.2=n_ 12. If the highest point on the curve y : K — 3:2 — 4a: is on the :c—axis, then K : fltv-Z'X-l}, £30 Vow Xt—Z A- 0 cl»: M 2 ®_4 Wl/vlm X=—2 %:0 —> O:l<—C—2)—.4(42) C. _2 K:-—-4— D. 1 E3 1,..- MA 165 FINAL EXAM Fall 2005 Name: +_ Page 5/8 13. A linear approximation shows that (16. 2)% is approximately Mu) {(a) + Ham (1) for 'x new- a— 3C(x)=x% a: 16 A' 2+; {’00:}. 1x34 B 2+% 4 §(15):16’/4= 3/ c +1i6 §’(l6)::}'- 06)- 4;}, __’§.._.. :1 %‘—2 . D. 2+5 —\((x_ -3)“ +x —\l>< €on+25~>< = - ”+2193. \/§ 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 of the shuttle. When . 7r . . . . 1 . . that angle is 1’ it IS increasing at the rate of Z radians/sec. How fast is the shuttle rising at that instant (in miles/sec)? -Tr 01.8-1 /,/ Tl WW 9'? SE '2: A. 2 9 '41 Fine) .53, wkun 5:}; .15 '6“— 3 —--~->l 170*)97'2,‘ C. 1 2 see- :Ld D.1.2 E. 1.75 MA 165' FINAL EXAM Fall 2005 Name: , Page 6/8 1 1 1 16. / 3361-2613:: “f ‘eucLu, :. .L a“! ._—_ .Le -1 0 7, 2. 2 o A i M= >< __ e-i “ 2 An=2xAl>l ‘ 2 @e—l 2 X20-«vu: x=1 “£1.31 C 6:1 D 8—2 62*1 E 2 e 1 4 1 3 3 1 17/(n$)dx=fuolu:_‘£. :2. 1 5’3 o 4 4. 1 LL:me 0 A E omzi—ckx e 7‘ 1 ('6 G) @Uow .LIH 0 ‘1. 1 18.] a: x+1da3= ( u—I (:4;ng 3/1 Va. -1 V 0" ) (u —u NM 0 u:x+l. , 5/; 3/ 4 A _i u‘l ' 3 clM=ClJX ff.“ -- ~—-—-3 " 4 6 _. - B. —3 x:u—1 2; a" 0 4 y:—1-.u=0 ‘ 2- 2 ~— ...4 0 _§ x=o~u=1 ‘75-: ’ \f .*% E _l ' 15 19. Find the absolute maximum and absolute minimum values of the function f(a:) = 23:3 + 33:2 — 122: on the interval [0, 2]. -§'/(X)‘:CXI+6X —l‘2 :Q(x1+X-2): 6(x+2)()<'1) §’(x):0 \Llnlm x=—?_ m37<=1u But -24 {0,21 . max 4, min —3 . max 3, min 1 €<°)=0 {-(1):2+3—32:—-7 maxO, min —7 {(8:23 +3’4‘“2'2=4 ©max4min—7 A B 4 C. max 2, min 0 D. MA 165 FINAL EXAM Fall 2005 Name: Page 7/8 fl 2 20. If F(x) 2/ ct dt. then F’(4) : 0 A. 62 a. F/(x) - €05) ' = ex 3‘ e4 ‘ m 26? © a " 4 : : —-—-— D.‘ g o 2.2 4 ‘t. E. 67 21. If f(:1:) =‘ (ln$)$, then f’(e) : 1 _g(x)=eren(lbnv)x.= €XQ"(’(M'") B e 4m in — 1 you = 41" l ‘0 L,‘ .L. .1. + Mao] C e ‘me x D 65 I e-Qmaxne) e = 1- E 2 H) e, .. [W* Lanna] ':: € (1. +0) : i 22. The area of the region between the graph of f(x) : $521+ 1 and the m-axis, from :c = 1 tox=\/§is {'3— ...1. {—3 A Z A : j __L__ (bx -: tam x) 6 x721 1 4 1 1 a 12 : film 5 —- Town" C g = I. I: :11: D 5 2 4 ’2. E f I 3 23. The half—life of a certain radioactive substance is 10 years. How long will it take for 18 gms of the substance to decay to 6 gms? kt M10 n1(t):ma€ lav-m0 :mo 6 A. 6ln10years lo. _ ‘.€nzu=_k10 "’ k="'€—Zé B. 101n6years h m 'l' :m E ----~1" () D ID -Lmi C. 101n_3 years Find t 80% 6:486 IO ln6 J. _ “Mt D. 18ln10 years 3 h 15: 13 —€ 3:—......?: t _n_ n M ® 101I12 years tzaobw‘s MA 165 FINAL EXAM Fall 2005 Name: , Page 8/8 24. The. focus of the parabola .172 + 2.1: — y + 3 = 0 is at . )(l2 + 2 x :: ké~ 3 A. 25. The ellipse 9:102 + 43/2 — 362: + 8y + 4 = 0 has vertices at the points 94444 + )+4(41+23+ 4:44 A <2 .4444) 7' (— 2,— —)4 and (~2,2) 9 (x3 4x +4) +— 4 (‘5 :2\;5+1):— 4+3Q+4: (_ 271) an“ 2 6) 9 (x—zffll- +(\3+1)=3G . D (42,2)and(, 2) &,2)1+ (43+)) 1:1_ . (ED (2,—— 4) and( ,2) 4 . 9 Center (2,4)] (1:3) b:‘2 ‘4 4: ._,/M‘(‘12'1+3)=(?,2) flC(2,«»> . j; W2, —!-3):(2) ~42) ...
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