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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 $062).
a. 1 '
b. 62
'c. e d.0 6 +00 5. Find F’(£c) if my) : Eng. dt
a. 1/1119:
b. 111011213) 0. (111:1: d. 1:” 1/011 1
e' mlnm 6. Use the midpoint rule to compute R4 for the deﬁnite integral 5
/V2:U1dw
1 a.1+«/‘3’+¢5+x/7 b .2_§ ' 5.3 Cx/g+«/5+\/7+3 61.2;— " e; £2 + x/é + x/é 7. The velocity of a bob moving along the m~axis on a spring varies with
time according to the equation v(t) = 1016 — 3752  10 At t = 1, the position of the bob is 20. Which of P, Q and R is true?
P: 5(2) :2 18 Q: 3(0) 2 26 R: 3(4) 2 2
a. Only P and Q are true
b. Only P is true
0. Only P and R are true d. Only Q and R are true
e. All are true 8. Let Abe the area bounded by f = a???) and the x—axis on [—1,3].
Using the maximum and minimum values of f = on [—1, 3] determine
which of the following is true. a.'OSA_<_4e2
b. 4_<_A_<_4e9
0. 463143469
Cl. OgA_<_'4e e..ziegA__<_4e2 9. Find 3% [:3 cos(7rt2) dt g
a. sin(7ra:6) —— sin(7r:L2)
b. — sin(7ra:6) + sin(7ra:2)
c. cos(7ra:6) — cos(7ra:2)v
d. 33:2 coS(7r:1:6)  cos(7ra:2)
e. 3222 cosh:03) 10. Evaluate limm,_++00 milli— x/E)+1 ﬂea a. 1/2 M b. 2 v Q c. 1n2 ' d. 1 e. 0 W 11. Find the area bounded by a: = —1,$ = 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 {Isaxis. 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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