Fall 08 A - MAC 2311 TEST 4 A FALL 2008 2 fig 5 W C;A Sign...

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Unformatted text preview: MAC 2311; TEST 4 A FALL 2008 2 fig 5 W/ . C;A Sign your scantron sheet 1I1 the white area on the back 111 111k.) B Write and code 1n the spaces 1ndlcated .55. L, . 1) Name (last name, first initial, mlddle Initial) 2) UF ID number " i 3) Dlscuss1on section number ffzh’fC Under spec1a1 codes” ,code In the test ID number 4 L 12 3 ' 5' 5 5 5 7 5 5 - 5 , 523 42 5f .6 '7 ’8' "97' 09!" :D At the top right of your answer sheet for “Test Form Code” encode A‘.5 E This test consrsts of 11 five—point multlple choice questions 3 one—point and 1 two-point bonus questlons and two sheets (4 pages) cf partial Credit ' questions worth 25 points. The time allowed 1s 90 minutes = 557.", E WHEN YOU ARE FINISHED: 1) Before turning in your test check- fort transcribing errors Any mis— _ _ L ' takes you leave 1n 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 MAC2311 homepage after the exam.) ' ' 1A NOTE: :Be sure to bubble the 31133133319 01.119811311891415 bn5youf scantren; . - . 1 ~ 1. Use Newton’ 3 method to approxunate \/—,~ 1131ng the functlon [ I ‘ f(az) = :03 -- 9 and startmg wish a; fir3't apprommatton ()f :01 =22. Then the second apprOximatlon 002e- -— : ~ ~ ~ . ~ , 01:0 usmg three sublnterva of; equal Wldth and . 6 1 2. Approxunate / 350 +‘ 11. , lettlng 20;? be the m1dp01nt Of Z'bmterval [302-1, :02] t 3. Find the area of the largest rectangle Whlf‘h can be formed between the 1 , :0- and y—axes and thegraphofy 6—53 ... = ~ .. ‘- 4. The slope of the ta11ge11t 1111e t6 the curve y f (a; ) at any pomt is g1veI1 _ ‘4 7‘ bym ~2— -— 413.11 the curVe passes threugh the 1501111: (1 3) 1111(1 f (2) a-Z ., b 1114*?) ‘0 1114—5 d 1112+ 3 , e". ... .1 ., 2 , _ -1 + 3:2 ..... 1 3] ‘~ and use them to find the upper and lower bounds for the area A of the ' ,. a, ,_ , , Ieglon bounded by f (as) aud the :c—axis on [ —-—2 3] 33]}1 Note that A1=_j_3/ . 1 ' ’ ' . , ., ' . _,2 5 Fmd the 1111n1mum and mammum values bf f (as) 1313*i“1~* 1 1 ' -2 , 2 “93343113555%~1 .' 1r ' 6' Evaluate 2% 1/‘1+t3dt. ' , ~ W 3:64. as» __ . 2V1 + 336- 2(1+a:6)%._ 2(1 +x3)% (VT?A~¢?EE.” a“ 13334» _ 3:02 , 2 . 2W 2W e. me—m_ ,b, 3A ' 7.‘ Evaluate / _ 5 2 35.1 a. Ina~ 5 . b. }; c 4+lng- '5~d._'3"+ln41‘ e 3.;11‘1‘51‘: _ 1 8. Find the area of the region bounded by the :c—axis, the graph of ' Ina: - rm: ( ) ,the lines :13— —— e and .a: = 6-21 ‘ '5 9. 'A particle moves in a Straight line so that its velocity at time t is given 5 ' by v(t)- — t —— 2 centimeters per second Find the displacement of the p 1 particle and the total distance travelled on the time interval 0 < t < 5 13 - ~~ y- g? cm; ., 15 ' . ’2“ em = ~ - . 13 ~;5'7-r ; .075; ID. If / f(:1: )da: —- / f(:c) ddz- —— f f ac) das, then Wthh 0f the Iollowmg ’ statements ls/are true? . ' ' “ ’ " ' ' " ‘ P The eqfiatlon above IS true II a— —‘ 2 afid b: 5 Q If/ fm)dm—4and/f das—Bthen/fvaR-I ' b R. If lbw dos—3 then/(2f(m)+l)das——b+5 Be fibre to WeIkIthe bonus pIobIems on the next page.- ' 5A Bonus!!__ .1 Questions 12 14 (1 point each): Rubb1e a font'rue'and b 191‘ false. 6 ’ .12. In approximating a zero of the equation f (as) —- 0 Newton’s Method I ' uses the m—intercept of the tangent 1111s to y: f (cc) at (m1,f (331)) - .. ‘ as the approximation $2. _ , . i ,. . I ~ a. True -, I b. Fa1se_‘ 1 . I =‘ " " . 3 /1+$2dm 1nl1+zv 1+0 * a. nae 1:»;b'.;Fa1se;gP I ' 14. The area of the region bounded by f (:0) —- 333 and the as—ax1s from {13“— —2 i ‘ tox~2lsg1venbyf at 3am. {#2 I ' aTruebFalse '15. (2 pts. ) Evaluate the followmg limit of Riemann sums by first wr1t1ng ,' p it as adefimtelntegral lin1 ( +22)2 ('77:); p ‘_ . 711—105z 5.6 7. 6A?" MAC 2311 Test 4 A Part II Fall 2008 Sect# Name U.F. ID Signature SHOW ALL WORK TO RECEIVE FULL CREDIT. A piece of land next to a stream is to be divided into three adjacent fields and then fenced so the fields contain the same area. The fencing for the side opposite the stream costs $6 per linear foot, and the fencing for the sides perpendicular to the stream costs $3 per linear foot. Find the dimensions that will minimize the cost of fencing material if the owner Wishes to enclose a total area of 800 sq. feet. 5fr€amcno fence? l 1 Function to be minimized: X l/ Constraint: ” Use the Second Derivative Test to confirm your results. 7A 2. Consider the area under the curve f (m) = 233 + 312" on [0, 2]. a) Find a Riemann Sum which approximates the area using n subin— tervals of equal Width and :13: = right endpoint of the subinterval [mi-*1, 33¢]. 71 .23 . 2:1 b) Find the exact area under the curve f (33) = 2:10 + £132 from a: = 0 to m = 2 by taking the limit of the Riemann Sum as n ~—> 00. TL 71 2 Note: 2 2' 2 71012—1» 1)7 2 2,2 : n(n + 1)(2n+ 1), 2“: 2,3 :[n(n2+1)] i=1 i=1 i=1 6 Area: 8A Sect# Name 2. ' (continued) 0) Check your answer in (b) by evaluating a definite integral, to find area. Area: 3. Evaluate each of the following integrals. a) / cot(2m)dzc 9A 4. A point moves along the m—axis with acceleration ‘ 2 . _ 2 2 W > , a(t) (2t + 1)2 1n/sec for t _ 0 a) If the initial velocity is 4 in/ sec, find the velocity function v(t). v(t) = . in/Sec b) Find the distance traveled between t 2'0 and t = 2 seconds. inches 10A ...
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