MAC2311e4 - E MAC 2311 — EXAM 4 SPRING 2006 Sign your...

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Unformatted text preview: E. MAC 2311 — EXAM 4 SPRING 2006 Sign your scantron sheet in ink in the white area. on the back. . Write and encode in the spaces indicated: 1) Your name (last name, first initial, middle initial) 2) Your UF ID number 3) Your discussion section number . Under “Special Codes”, encode the test number 4, 1 . At the top right of your scantron sheet, for “Test Form Code”, encode A. o B C D E This test consists of 8 four-point multiple choice questions, 4 two—point multiple choice questions, 1 four—point bonus multiple choice question, and four pages (two pages front and back) of free response questions worth forty points. The time allowed i390 minutes. WHEN YOU ARE FINISHED: 1) Before you turn in your test, check carefully for transcribing errors. Your responses cannot be changed after you turn in your exam. 2) You must turn in your scantron and free-responsa portion of the exam to the proctor. Note: Problems 1—8 are worth four points each. 1. Evaluate: [14 (f— ")2 dz 2. Over a seven-day period, the number of sea turtles present at e. beash changes at 12 a rate of 12. -- —0 turtles per day, where :z: is the number of days after that {1 + 29:)2 have elapsed during this period. If there are 120 turtles initially, find the number of turtles present after 7 days. A. 148 turtles B. 160 turtles C. 208 turtles D. 232 turtles E. 316 turtles 3. Approximate the area on [0, 2] hounded by the :t—exis end the curve 3; = 4:” by using a. Riemann Sum with 4 subintervals of equal width and 33’; = left endpoint. A. 5 B. 1—25 c. 10 D. 32-5- E. ’15 4. Find the valfiie of c guaranteed by the Mean Value Theorem for the function f(a:) = 1+ E on the interval {1,3}. A. fl B. 3 c. «5 D. calm .17 w 5. Calculate the exact area on {—1, 1] bounded by the x—axis and the curve A.2 B.6-—2e 0.6—1 D.5+28 E.4 01 v5 6. Calculate: —--/ 2:31:1(1 +az) d3: dzc 3 A. 2fi1n(1+¢5) B. ln(1+\/E) C. fi1n(1+:c) 2 2J5 13' fi(1+\/:E) E' 1+x 7. Asli rocket consumes fuel at a rate of w(t) = l +4tel“2 liters per minute, where t is the number of minutes that have passed after Hftofl. Find the amount of fuel consumed within the first minute after liftoff (t = U to t = 1). A. 3 liters B. 4 liters C. 8 liters D. 2 + 8 liters E. 26- —— 1 liters - 1 8. Calculate. jm d3 A.2\/E+ln(1+\/E)2+C B.2fi1n(l+fi)2+0 C. *2 +0 1+x/5: 1 2 —2\/E 13.2 — .«~——- —— fi+2lnlrl VEH: E. 3(1+\/E)3+C Note: Problems 9—12 are Worth two points each. a; 2 9. Evaluate: / W dt 0 6032(1) A.1 B.4 0.71- D.7r2 E.1+7r “ z' 1 1i}. Identlfy the defimte Integral represented by the hunt: ”11.15.10 2 [2 + 5111(1 + E )] H |,= 2 2 2 A. / ms'm(:r:) dx E. f 2 + sin(3:) dx C. f sin($) dz: 0 1 1 1 2 D. f 2 + sin(:t:) d2: E. / sln(:t:) d1: 0 0 :c 1 _ 2 11. Let 0(3) = / g(t) :11! where 9(t) = flit-5:2}; Which of the following statements —2 are true? I. (9(a) is increasing on the interval (“2,2) . II. 6(3) is an antiderivative of 9(3) . III. C(x) has a. local maximum at :1: = 4. A. I only B. III only C. I and II only D. II and III only E. I, II, and III 1r 12. Evaluate: / I 003(9)) | dac (Note: drawing a picture may be helpful to you.) 71' A. 0 B. 2 C. 4 D. 8 E. 16 Bonus!!(4 points) 13. The graph below represents the rate at which a population of foxes changes over a six-year period. Horn the choices below, choose the best estimate for the total change in population over those six years. hundreds at 40er Per [For A. 200 B. 400 C. 600 D. 800 D. 0 _\[A('.‘- 2311 ——— EXAM 4 Free limponsv Mlilc____ H SECTION __ UF ll)_ 'l‘EST mRM com“; A YOU MUST SHOW ALL. OF YOUR WORK TO RECEIVE CRl—LDITH » ) 1. Examine the definite inmgml / 31* — £3 (if. 0 .-\mn'nxin\7iw the value of tin: inwgml using; 21 Rionimm Sum with rwu .cnbinrermla (11' (1411le Width and .1‘7 2 i‘i‘lidpuim. Lieu ('Hl(‘lllllh to find the niaxiintin'ii’zni and minimnmfl/i \‘fllllt‘ on [(1.2] and Limit {150 the (-uinparim1'i {)I'Upf‘llfi' of integrals to find 111mm and lowm‘ lmiunis for Ihv inwgrzil, TI 1 ‘— IU -_ 2 _ ________ :‘i/ 31 — I3 (ix 3 __.__ ________ _ I] Write an oxprvssion below for the integral as a limit of Riemann Sums: 2 Sir .1'3 (.il' : Jim 1 A L Evaluate the limit of Riemann Sums that you wrote above. Use the fbrmulas: )1 7! , ~. ,1 ~. . l7. . . ') . 7)(\n+1) ,2 _ mn — 1}(3n + 1] ,3 __ rn(n — 1) ~ 21: T Z) _ —'6— Z! __ i 2 . r—l ILL Chm-k your unswm' by ovnlum iug the integral once more with rho lep of Ihu l-‘nmlmnental Theorem of Calculus. 2. I\' A .\ I E____ Calculate the il'ltvgmls lwlr'aw: /" V/L +' 311111) 1 —— «r 1 2f 1‘: 2.1-) .1 (11- x H . ' (t‘ ._‘ ".- Bonus: [wg— ( I = . {1+ sunk/1H2 SECTION_ 3. A tiny 111011101119 travels in a straight line through a blood vessel so that its velocity After 1 hour:- have passed is L-‘(tl =—» 15( t V"? — Jr) centimeters per 1101111 Calr-ulate the displacement of the molecule during the first: four hours of its nmlion. ( S i 111111in 1-1 111 1‘ ans wer .) ('fal(>l.1l-(1te the fowl distance travelled by the molecule during the first four hours of its motion. (Simplify your answer.) If the IIlOle’lllC has returned no its original position [.5' = 0) after 1 hour has passed, calculate 11:4 position 3(1) at every time fl Wlmi was its initial position"? ...
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