Fall 07 - MAC 2311 w FINAL EXAM FALL 2007 | A. Sign your...

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Unformatted text preview: MAC 2311 w FINAL EXAM FALL 2007 | A. Sign your scentron sheet in ink in the white area. on the back. B. Write end encode in the spaces indicated: 1) Your name (last name, first initial, middle initial) 2) Your UF 1]) number 3) Your discussion section number 0. Underi‘gpecial Codes”, encode the test number 5,1 . D. At the: top right of your scantron sheet, for “Test Form Code”, encode A‘ .‘3BGDE : i E. This test consists of 23 five-point multiple choice questions and 2 five-point bonus multiple choice questions. The time allowed is 120 minutes. F. YOU ARE FINISHED: 1') Before you turn in your test, check carefufly for transcribing errors. Your responses cannot be changed after you turn in your exam. 2) You must turn in your scantron to the proctor, but you can keep the exam questions. i J a i Note: Problems 1—25 are worth five points each. 1. Find the slope of the tangent line to the graph of f (cc) : 4(33 w» M55)? at the . point with m-coordinategtl. ‘A4 E6 08 010 Km E r 2. Which shape below best characterizes the graph of Mac) 2 937 —— x5 —- 2:4 near the point P on the curve where's: 2 1 ? , ‘ f r ‘ P P ‘J A. \\ B. r C. {/4 D. L E. none of these i 1 82m m 53; 3. Evaluate the limit: lim ewe—“~— m~>0 e3” "— :L' m 6”“ AA 3 1 CHIP—4 ,5». Gilt—I E 2 4. Calculate the exact areaijon [—-1,1] bounded by the 3:»axis and the curve 1 1‘ ‘ 1 $24-19” 3350 HQ“ 1 1+\/E m>0 Afi asmé Ce+1 Dew2 Eéme ' 1 5. The equation my — Zfi m 2 la(y) defines y implicitly as a function of 23. What is the slope of the tangent Zine to the curve at the point (4, 1 ) ? ' ‘ A. m s. g c 1:). 00101 E75 sole: 1 f6 6. A rocket érises upward from the ground (initial height zero) with acceleration given by a(t) : 60': III/82, after t seconds have elapsed. If its velocity is a recorded: as 200 m/ s after one second has elaysed, what is the height of the rocket above the ground at that time? 1 A.120tn 13.140111 C. 16011: D. 180 m E. 200m F ’7. Evaluateéthe definite integral: [4 seo2(6) 1311209) d9 L Q (3 8. To adfieve a special effect, an elevator that is ascending at 10 ft / sec is filmed I by a cameraman that is moving away along the horizontal at 2 ft/ sec. At what rate is the slope at of the dotted line (pictured beiow) changing when meioeianay=2sfti2§ 1 t E elevator A. 0.2 visits/sec 1340.8 units / sec I B. 0.4 uhits/sec E. unit/sec ‘ C. 0.6 units/sec l a: 9.. Evaluate the limit: 11m [2m ~ 322} . 53—4-0 i 1 i 1 B. 2 C. e D. 32 E. U i ! 16. A spherieal cloud of gas is observed in space. Use differentials to estimate the erroriin using a measurement of 3 miles for the radius to calculate the volume df the cloud, if the measurement may be off by % mile. A. Qtr 1113.3 B. 12w Em? C. 18w 11113 ' D. 367: me E. 54% mi3 - , 11. The height (in feet) of the water at a particular dam is represented by the continuous function L(m) : 3(m2 _ s + 10", where x is the number of weeks that have elapsed from the present. Find the value of M + m where M and m are the maximum and minimum height of the water respectively over the next twogweeks. gem 13.5ft cse om- see 12. For the shaded region, is known that the length of s is a function of m given by s = A 1 /1 ~i- % dt. Find the rate of change of the perimeter of the-shaded region respect to miwhen a: = 1, if the iengths are measured in meters. A. x/fi {mz/m 2—? mg/m : 5 3.2+fim2/m E 3—dgm2/m lnlxl 13. What are the vertical asymptotes of the graph of f (m) m ? :1: -— 1 ; A.m=:00nly B.m=0anda:=1 C. ct: = 1 only I). there are none . 3 14. Classfiy the local‘extrezna of the function 9(a) m a; 4 . A. no relative maximuim B. one relative maximum one relative no relative minimum E ‘ E C. one relative maximum D. one relative maxima one relative nainimaj {we relative minimum 15. Evaluate the following limit of Riemann Sums by writing it as a definite I integral. 11m ::(n)(li |~ n) n»—->oo I 2:1 I ! I . i l P” awe: 7 B. E3— C. m I). {D CAMEO ' l g l , 16. Calculate the exact area square units) bounded by the m-axis and the graph of the" function fix) = 8 on the interval [ 1, 4] . Warning! This function a is both negative and pofsitive on the interval. ' E B. E. 2 O pad-e 53 tot—4 ! l 1 i l . » l I z 17. A particle in a magnetic field travels in a straight line. The force (in Newtons) acting upon it is given by the function F m \/§ + 32, Where s is the position ' of the particle in meters. At what rate is the force changing with respect to me when the particle at position 3 = 1 and has velocity 4 m/s. 'A.GN/sec : 8.6N/sec C.8N/sec D. 10 N/sec H.12N/sec 18. Use Newton’s method With the first approximation :61 m 1 to find the third approximation 223 of thefroot of the function f(22) = 3:3 — m — 1. 5 11 .A. 5 Bi. —— c. mioo .U phi-x! to tote: 6 19. The rateof honey output from a beehive at any given instant is given by 1' 1 : _ w(t) = 100 + (1 Easy mflljliters per week, where t is the number of weeks that have passed from the present time. What is the net amount of honey produced over the firSt four weeks? F i 1 I E , A. 360 IhL B. 400 lmL c. 440 mL D. 480 mL E. 520 mi. 20. Find thejm-coordinate ojf the point on the curve y = v1 + 2x? located at the shortest gistance from the point (2, 0 ). D.\/§ E.2 75> NJth 335 (JOIN ('3 5...: 2.1. Evaluate W(1) if itis known that 3?; = 8w(m2 "— 1)% and W(O) m 2. A.1 3.2 (3.0. A D.—-2 3—1 22. Detennine the vaiue of the constant c that makes this piecewise-defined function continuous: F ix! m<0 Iii-{~33 em+c_ 3:30 3g A} E32 (3.0 13—2 E~1 23. Suppose that the blood sugar level of a certain individual is modeled by L(t) : 100 +' 4015 — 153 points, where t is the number of minutes that have , elapsed after eating. Find the rate at which the blood sugar level is changing _ after 5 minutes, and the average rate of change over the five-minute interval. ‘ _ a 1 l A. instantaneous rate: 1«35 points per min; average rate: 15 points per min t [ C. instantaneous rate: f3?) points per min; average rate: 35 points per min E f B. instantaneous rate: points per min; average rate: 75 points per D. instantaneous rate: #15 points per min; average rate: 35 points per'min E. instantaneous rate: 4—15 points per min; average rate: 15 points per min i i t BonuSIKS pts each) 1 18m _ 24. Evaluate f0 (:6 + as (ice. 9 5 3 ' 1 1 A. ~8- é- C. E D. 1 E. i B. l 25. Of the graphs of the fumiitions listed below, which have both of the horizontal asymptotes y 2 $1 ? ' 1 — em - a: 2 I. fix) w 1 + em 119(22): m HI. Mrs) : 2; arctan(x) ! i A. only B. II only C. I and III only D. II and III only E. I, II, and III YOU HAVE REACHED THE END OF THE EXAMH E - THERE ARE NO PROBLEMS ' ON THIS PAGE: ...
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This note was uploaded on 02/10/2011 for the course MAC 2311 taught by Professor All during the Spring '08 term at University of Florida.

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Fall 07 - MAC 2311 w FINAL EXAM FALL 2007 | A. Sign your...

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