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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 twopoint 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 onthe 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 [3021, :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) aZ ., 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: = 621 ‘ '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 ~;5'7r ; .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/fvaRI ' 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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