Spring 08 - MAC 2311 TEST 4 A SPRING 2008 A. ' Sign your...

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Unformatted text preview: MAC 2311 TEST 4 A SPRING 2008 A. ' Sign your scantron sheet in the white area on the back in ink. B. Write and code in the spaces indicated: ye. ,% {a gen as” 1) Name (last name, first initial, middle initial) 2) UP ID number 3) Discussion section number (3. Under “special codes”, code in the test ID number 4, 1. ' 1 2 3 a 5 6 7 8 9 0 e 2 3 4 5 6 7 8 9 O D. At the top right of your answer sheet, for “Test Form Code” encode A. ' a B C D E E. This test censists of 11 five—point multiple choice questions, one five—point bonus question, and two sheets (4 pages) of partial credit questions worth 25 points. The time allowed is 90 minutes. F. WHEN YOU ARE FINISHED: 1) Before turning in your test check for transcribing errors.» Any mis— ‘ takes you leave in are there to stay. 2) You must turn in your scantron and tear off sheets to your discus— sion leader. Be prepared to show your picture ID. with a legible signature. 3) The answers will be posted on the MACZBll homepage after the exam. 1A Problems 1 - 11 are worth 5 points each. 64“” —- 1 sin a: 1. Evélua‘te lim$_+0 a... ‘0 .b; 4 c. 1/4 (:1. 1 e. does not exist 2. Find a and b so that 'bd ‘ I 10 U 20 / f(a:)dm—- f(a:)dw= f(m)da: a ., I 20 1 -a.a= 6:20 b.a=20 b—‘=1' c.a=1 b==10 d.a==lO 6:20 e.a=;10 5:1 3. Find me) if mm) = £21- and fa) = 3 (B a. f(:c)=:c_——ln{:c|+2 b. f(m)=ln]tw+1'[+3‘ 2 0- flat) = a? +3 ' ‘ ‘ f d- f(w) = 202/4 + 22/2 + 9/4 _ if e- f (as) »= m f- ln'lml + 3 4. EValuate limwfié $062). a. 1 ' b. 62 'c. e d.0 6- +00 5. Find F’(£c) if my) : Eng. dt a. 1/1119: b. 111011213) 0. (111:1: d. 1:”- 1/011 1 e' mlnm 6. Use the midpoint rule to compute R4 for the definite integral 5 /V2:U-1dw 1 a.1+«/‘3’+¢5+x/7 b .2_§ ' 5.3 C-x/g+«/5+\/7+3 61.2;— " e; £2 + x/é + x/é 7. The velocity of a bob moving along the m~axis on a spring varies with time according to the equation v(t) = 1016 — 3752 - 10 At t = 1, the position of the bob is 20. Which of P, Q and R is true? P: 5(2) :2 18 Q: 3(0) 2 26 R: 3(4) 2 2 a. Only P and Q are true b. Only P is true 0. Only P and R are true d. Only Q and R are true e. All are true 8. Let Abe the area bounded by f = a???) and the x—axis on [—1,3]. Using the maximum and minimum values of f = on [—1, 3] determine which of the following is true. a.'OSA_<_4e2 b. 4_<_A_<_4e9 0. 463143469 Cl. OgA_<_'4e e..ziegA__<_4e2 9. Find 3% [:3 cos(7rt2) dt g a. sin(7ra:6) -—— sin(7r:L-2) b. -—- sin(7ra:6) + sin(7ra:2) c. cos(7ra:6) —- cos(7ra:2)v d. 33:2 coS(7r:1:6) -- cos(7ra:2) e. 3222 cosh-:03) 10. Evaluate limm,_++00 milli— x/E)+1 flea a. 1/2 M b. 2 v Q c. 1n2 ' d. 1 e. 0 W 11. Find the area bounded by a: = —1,-$ = 7r/4 and the m—axis. ' __ seczsc ifmZO f(m)"{1—m2 ~1fm<0 12. (Bonus!) Three adjacent fields are to be fenced with 1200 ft of fencing so that the total area enclosed Will be a maximum. What values of w and y should be used? ' a. an 2 200 y = 300 b. a: = 50 y = 300 c. a: = 150. y .’=110’O ' d. a: = 75 "y = 150 e. none of the above MAC 2311 EXAM 4 Part II Spring 2008 Section Number " Name UF ID Number Signature SHOW ALL WORK TO RECEIVE FULL CREDIT 1. A square is to be cut from each corner of a piece of paper measuring 4 inches by 4 inches, and then the sides are to be folded up to create an open box.What size square (dimension :1: by so) should be cut to mazimize the volume of the box? Function to be maximized a: = in. What is the second derivative of the function? Use it to confirm that you have found a relative maximum. 2. For the function f 2: 111(m) — m. Complele the following: a) f’($) = b) f(a:) has a relative ~ at e) W) = l d) f(:c) is concave down on e) 11mm“ f(w) = * f)limm.++oo Ax) = 3). Sketch the graph of f 3. A particle, initially at rest, moves along the {Is-axis. such that its acceler— ation at time t > 0 is given by a(t) = cos(t). At the time t = 0, its position is w =: 3. ‘ a) Find the velocity function. v(t) = b) Find the position function. 3(t) = c) Find two values Where the particle is not moving. 4. Use the definition of the definite integral to compute f01(2a: —— 1) dw. Some formulas: 22:1 k; = EVE—+1) 22:1 k2 ___ n(n+162(2n+1) The integrand f is Am 2 Using right hand endpoints in: = R” = 22:1 Compute limnnoo Rn = ...
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Spring 08 - MAC 2311 TEST 4 A SPRING 2008 A. ' Sign your...

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