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2000 sol - MA 165 FINAL EXAM Fall 2000 Page 1/9 NAME...

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Unformatted text preview: MA 165 FINAL EXAM Fall 2000 Page 1/9 NAME gOLUTIONS STUDENT ID # RECITATION INSTRUCTOR RECITATION TIME LECTURER INSTRUCTIONS 1. There are 9 different test pages (including this cover page). Make sure you have a complete test. 2. Fill in the above items in print. I.D.# is your 9 digit ID (probably your social security number). Also write your name at the top of pages 2—9. 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 or calculators 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 student ID 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 w your test booklet to your recitation instructor. MA 165 FINAL EXAM Fall 2000 Name: —_ Page 2/9 2:2 —:1:—6 = Qim (x1327 (X44) 1. ' :13}? 23—3 x—a'a X'3 A. Does not exist :bmcx+2)=5 .5 x__,? C. 3 D. 1 E. 0 2. The domain of f($)=«/1—1n(2—x) is “(2’30 'V’ (Ll/JVQJ for“ 2-x>O : 1X<Zi A. m<2 Vi-bn(2-x) in alpha {m B- -2Sx<2 1— Qm(z~><)zo C. 2<:1: 13/”(2wx) 3 4- ......W D. 2—e < a: 9""5‘ $6 21:3:sz @2—BS$<2 2 —€_ 6 x < 2. 3. If f (x) = |a:|, choose the correct statement. ® f is continuous but not differentiable at a: = 0 B. f is differentiable but not continuous at a: = 0 C. f is differentiable and continuous at :1: = 0 D. f is continuous but not differentiable at :1: = 1 E. f is differentiable but not continuous at a: = —1 4. Assume that y is defined implicitly as a difi'erentiable function of a: by the equation (1 $3 — 2323/ + y3 = 7. Find l at (x,y) = (1,2). dz: 3Xl—X2‘iéi «74% +33‘Zé’fl‘30 (23:11- “ v ,m 3‘” — . 7 Ar(’~3)’(’/Z)u 3~1 ~L€i£x,2.1-2+3.4 337,0 C. 2 11 fl. -: 4. D' g abx E. 2—11 MA 165 FINAL EXAM Fall 2000 Name: _______— Page 3/9 5. The equation 1:3 + 10:1: + 1 = 0 has a root in the interval \l ' are “W “" ‘“‘ (9 (4,0) £6?) = '27 ”3°”L ‘56 C. (0,1) 9") = i >0 .; moi Rh CLO) E. (2,3) 6. The equation of the tangent line to the graph of y = sin—1(2m) at the point where 1 . 117-le 01” 1 -—(2x)7' 2 1 4 B =__ £_____ At sz: db}: 2’ I-tf‘ y 3x+6 2 3 4 IX $-31 J ‘4' 4 -‘ [email protected]=ix+:__1_ W kg—giw ‘(2,“;):Sm $14 3 6 3 qnwodv’nw o Lame/wt [4'in D y=z+1_l E 47 4 3 4 L -— ': __._ )( ——::. A Q ‘5’ 4’ E y=\/§m+£——‘/—§ 0‘6 %— iy +3-4— 3 4 " \5 c. V2 1 . f(=v)- f(2) I 7 Iff(a;)—:z:+; then:%1m_2 = 3C (2.) / '— 1. .L b5 A1+AVH.I‘V‘ A. % g”? - 3;; 13.; ’ ’L a. l— : :3— 0-;- i M " 4 + 0% [Um §{y)~ {1(7) E. Does not exist MA 165 FINAL EXAM Fall 2000 Name: ________ Page 4/9 . . Sihhx) 8. i ($263m(3z)) = X2 e CQS(3)‘)'3 d2} bihfsy) +2x€ A. 3$Zesin(32) +2$esin(3a:) B. 2226““(3‘) cos(3$)+3x265i“(3“’) C. mzesi“(3z)+2ze5in(3“) cos(3:z:) @ 3x2 cos(3:z:)e’i“(3”)+2xe‘i“(3z) E. $2esin(3$) +2xesin(3z) 9. The position of a particle is given by the equation s(t) = 3t2 + 621t + cos(1rt). The acceleration of the particle at t = 1 is Mt) = <50) : Gt +26%-1Tsin6'rt) A. 4+62_7r2 ' ’t ’2. 2 OWL)?- éfl‘tl: 6 +423 — o coSCrr’c) B. 6+2e +7r 0 9. ' C.1+e2—41r ‘2. , Cd!) 1: G +4€247 :0“ D. 3+4e2+7r2 26+4e +TT ®6+462+fl2 10. The lamp of a street light is 30 ft above ground. A man 6 ft tall walks towards the street light. If the length of the man’s shadow is decreasing at the rate of 2 ft/sec, how fast is he walking? MA 165 FINAL EXAM Fall 2000 Name: —_ Page 5/9 11. The linear approximation of f (x) = x/x + 1 at a = 3 is ‘/ ~l _l 90) C3: §<3>+§I(3)(X_3)1 A. x+1~2z 2,forxnear3 +0? x W‘, 3 B. \/x+lz%z+%,formnear3 E3) 9* ©V$+lzix+iforxnear3 [S/(X; l. D-x/$+1~i-:c+i-,fora:near3 - ZVx-c-t E. z+1%%z—%,for:rnear3 ’ 5. its): —— q. §(x)’n‘1 9- 4" (”'33 at“? x W? 12. The absolute minimum value of f(:z:) = 3x2 —— 12:1: + 5 on the interval [0, 3] is §/(X):C>< -12 A.7 §/(X):O '. Q(xr'2.):O—+x:‘2. CVl'ttCELL .‘7 humlu/V ln(0,3) C _4 £(o):5 ’ D. 5 (3(1) :3«4 —-Q4+S :«7 é-0L'>.W!W.Valui E_ 3 86913.9 ’12’34'5 .1 ”4' 13. FOY' what value(s) of :1: does f(:1:) = e; have a local maximum ? x x i ’(x) x C ‘ e 2 A. :1: = 0 x2“ 1 x - B. :17 = — 15/0020 2 6 (x4) :0 2 x1 C. x=2 X 2 1 ‘W W owl»: Cv‘llu‘uxl D (L' = 1 ‘7 wuwnbtrr §/(7() < O Vtflv >< <1 ® There 1s no local maxrmum &’(y}>o {Av x>i gm :2. \p g “(ml mama T lfifiLNfi if, WEE} 29 CALL ‘Y‘M I° w \A 1“» MA 165 FINAL EXAM Fall 2000 Name: _________. Page 6/9 14. Find all intervals on which the graph of f(:z:) = coszc—sinm, —-§ < :1: <g isco d . 77 1r I ncave orvn a ("232) g m = ’sm - um - B (E 1) §”(x) :—oosx +">‘“X ' 4’2 ” _. ; sf 3:: ”term”! _£_£ Ezr— ‘l (XL—D h m :‘r C ( 2, 4),(4,2) £00?) <0 {or —II< ><< I: e4 13- Vii) 7. 4- 1r §’/(X,)>O “LAY L£<x41§ L E' (—5,?) 1 3 9m mac. (Lawn meg)? ' __ = \ X (I—L . - .- 15' ”133° (1 9‘) <31; 9 Y = elf-'YMWM" W A. 1 ' . 1—5; L" __£-___ J. B. Q‘m L; 5(1-1.)]:(Lm BELL:QM 1'4», x‘ e x XH‘” 1.. x-fim ‘1 @ l ‘Xflw ‘0‘ ’X ~ X: e o :QIY" __L_.:'l D. 00 Y‘ X-+°° lml; film I. L. -— ’1 E. —e X—aoo( Y) ' e 16. A crate with square base and open top must have a volume of 4 cubic meters. Find the height of the crate that has the smallest possible surface area. h...“ / VOQMW : 4- A. h=2 ‘ ll" leo :14- .h=1 fl ’ gwr'la 0 mm: 0- h=4 X A : x7” +4—xln D' h=§ " E. h=l A: X +4‘Xi 4 , x7- Pr: X1+ L“: X A,” : Q—x “ Lg? :- 31({3—8) 0le 3 7‘ 2 ‘7. - '- :— 41,“. :0 ”,(7‘ 80,0 .4 x (SLY x Q )<>O Win-7 (if—l <0 )Lov X‘Q 41x70 ‘ZDY (i7 MA 165 FINAL EXAM Fall 2000 Name: _._.____ Page 7/9 17. Find f(:c) if f”(a:) = e“ — sinx, and f’(0) = 1, f(0) = —-1. tat/(X); 6" + CJOQ'X .1, C1 @ f(m)=ez+sina:—:c—2 1603 1 :1 + 1+C1 “Cf-"‘1 B. f(x)=e”+sinx+x-—2 ; C. = ”—' —2 , 3‘ £00: €X+QO$X—-l, f(:v) e smx X _ C. D. f(a:)=e$+cosa:—3 £00 :6 +9'“X—x *’ 7, E >002 —L= 1 + o —-o +C2szt-2 S’CX) : ex-VW‘HX -—x —2. . f(:c) =e“+cosx—x 18 i zzestzdt— 3(2X) . d$ 1 — .2 32:2 42x7- A e I 28 B. 26612 C. 6122:2 D. e‘izzme3 @2612“? 11' 5' 3 _. , '2 19. / %ldx=f4(wsx ——Se< >00” 0 O f A ‘/— " —1 2 :(fithX’tth))4 + 0 B. fi+1 1 1 —.—. .— _ m o , o) c — ~75 a ( CD) 12—1 E. 1+; MA 165 FINAL EXAM Fall 2000 Name: _________ Page 8/9 20. Find the area of the region between the graph of y = xlha: and the x-axis froma: = e toz=e2. 7. e 2' 7' 'A. e—l A -; g i ok'x :1! *LdJJ. = Qmul me u I B. (ln2)+1 ‘1 x 1 QM 1 QM du-_Ld‘x 7' 2 _b" © ln2 u: x ' " '- 2N?- D 1 2 x=e «a u=1 (L ' ' n( +8) Xrfii—n ugine :2 E. ln(e2—e) 1 9. a: ,1 . 21 d — J U~ ._ -2 -3 __ fowl)” 1 u3&““]‘*‘“)9“A5 u2x+l clutch: ' M» '§ xtud 1 v=o‘——+url B' 2 K:| -—-)u='2 3 C. — ( —’ LL.)/2 8 " kL -"‘ —— -— .—___ 1 *1 -2. , ®§ : -J. ’ 2 E l ( U + 20.3)ll 4 _{_J_ .L _ + _ __ “' 2 g) ( l-I— 42- _ 1 1 E 1 I ‘2. 22 / tan Educ: f“ UM z—LL/‘I: l o :1: O 1' o 2. 4 7r UV: tam X he—L—‘J’JX A Z r+>(' MA 165 FINAL EXAM Fall 2000 Name: _______ Page 9/9 23. A radioactive substance loses g of its mass in 30 days. Its half-life (in days) is 3H) = £10) 8” Hack—g Ho) A. 151 2 E30 JgW‘Wekm .30fi8— ——.b«8:30k hk=,g;%8_ 0123 la): Wejimir 8.303; T? i“) 71:2 Ho) Mt E. 40% ~1- ‘ ”dime" w m “tn-:— 2%5‘ 1'...) 1130-178- 24. The focus of the parabola yz—Zy—Sx—23=0 is at the point 2 ‘1 :— 60) 0+3) A (—1,—3) (‘5’) + :3 affll B. (1,—1) Vwiw (.329 F © (—1,1) D (3,1) E (1,2) 25. Find an equation for the hyperbola with vertices at (4,0) and (—4, 0) and a focus at (_9)0)- AU) m2 3/2 A. 1—6 — 2—5 = 1 F0 um VCYI‘E‘K Vex it): :62 3/2 _ ””7 __ __ __ = (“7.0) 04,0) ’l ‘ 4,0) X B' 65 81 1 v . ‘ (tn 13v 2 2 T x y g C' 81 16 " 1 C2,: 4 x2 y2 C T: 9 rv r2 _ -_ _ = 1 1 z_ e_ ,1 PM, 16 81 «av-m ‘0'“ °‘ -15 $2 yz 1 EL '1" ’ _ _ _ = ...
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