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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: 1) Name (last name, ﬁrst initial, middle initial)
2) UP ID? number i 3) Discussion section number “(3. Under “special codes”, code in the test ID number 4, 1.
' 1 2 3 o 5 6 7 8 9 0
a 2 3 4 5 6 7 8 9 0 D. At the top right of your answer sheet, for “Test Form Code”, encode A.
' a B C D E E. This test cOnsists of 11 ﬁvepoint 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. 1. EVAIualfe limmﬁo elm—1 Vagr'o Y b: 4
1c. 1/4 (1.1 . e. does not exist 2. Find a and b so that . . blL‘. :‘ . I m / dac da: = dzc
a’ I; A, 20 ’ 1
A a. a: 1 6:20
b. a=20 [Jr—'1'
C. a=1 5:10
d.'a=10 62:20
8. a:10' b».=.==l V 3. Find my) if f’(a:) = £3 and f(1) = 3
' a. f(az)=m¢:1n1m’l+2 '
1b. f(ac) =I1n + +3  4. EValﬂate limwﬁd new). ' _ _ ~ , {Q
' X? b. e2
‘c. 'e
d. 0 ‘e. +00 5. Find F’(cc) if F(:1:) = ff“ ~t1 dt
3,. 1/1113:
b. 111(11123)
d.' 1 —~ 1/(11137)2
. 1 .
" wlna: 6. Use the midpoint rule to compute R4 for the deﬁnite integral 5
/\/2m~1dm
l
a.1+x/§+J5'+x/?
b 2§
"3
c.x/_§+x/5"+x/7+3
d. 26 " *e; ¢,..2+:2+\/6+x/§ 7. The velocity of a bob moving along the maxis on a spring varies with
time according to the equation ' we) ~._—— 1016— 37:2 —— 10 At t =2 l, the position of the bob is 20. Which of P, Q and R is true?
P: 3(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
c. Only P and R are true
(1. Only Q and R are true
e. All are true i 8. Let A' be the area bounded by f 2 6(32) and the m—axis on [f—l, 3].
Using the maximum and minimum values of f = on [—1,3] determine
which of the following is true. a.‘0§A$4e2
b.4gAg4e9
C.4€_<_AS489
d. OSAglle e.4e§Ag4e2 9. Find Eda—3 If cos(7rt2) dt
a. sin(7m:6) —— sin(7ra:2) l
h. —— sin(7ra36) + sin(7r:1:2)
c. cos(7rw6)  cos(7r:c2)_
d. 33:2 coS(7r:c6) —— cos(7m32) e. 3:132 cos(7rq:3') 10. Evaluate limw_,+oo Elfﬁg a; 1/2 , r «if;
b. 2 ' W :1. 11112 i ' .r
ya” v.4
2 e.O 11. Find the area bounded by a: = ——1,»:1c = 7r/4 and the m—axis. " __ sec2mifm210
f(m)7{1—m2 ~ifx<0 Nah4 V + 1n 3;.
1
b. 3 1
C.
d 5 ‘
8. who V 3
does not exist 12. (Bonus!) Three adjacent ﬁelds are to be fenced with 1200 ft of fencing so that the total area enclosed will be a maximum. What values Of a: and
y should be used? ‘ a. a: = 200 y =300
b. as = 50 y = 300 c. a: = 150__ v 3‘y100‘ . '
d. 92:7'5' 9:150 % e. none~0f the above '  MAC 2311 EXAM 4 Part II M
Spring 2008 Section Number  Name g?)
' UF ID Number
Signature
SHOW ALL WORK TO RECEIVE FULL CREDIT '1. A square is to be cut from each corner of a piece of paper measuring
'4‘ inches by 4‘ inches; and then the sidesare tobe folded upto' create an
open b0x.What size square (dimension In by ac) should be cut to mazimize
the volume of the box? Function to be maximized :13 = ‘ in. What is the second derivative of the function? Use it to confirm that you have found a relative maximum. 2. For the function f 2 111(3)) —~ :3. Complefe the‘following: a) f’($) = b) f has a relative ' at 0) f "(93) = d). m) is cogcave down on
3) limm—W'I‘ f0”) = ‘
f)1imrc—++oo f (93) = Sketch the graph of f 3. A particle, initially at rest, moves along the cit—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 :1: = 3. ‘ a) Find the velocity function. v(t)i I = b) Find the position function. 8(75) = ' c) Find two values Where the particle is not moving. 4. Use the deﬁnition of the deﬁnite integral to compute f01(233 — 1’) day. Some formulas: 2221 k = ﬂing—ll 22:1 k2 = n(n+162(2n+1) The integrand f is Ax 2 Using right hand endpoints =
Re 3 22:1 Compute hm”.+00 Rn = MAC 2311 ' TEST 4 B
SPRING 2008 A. ' Sign your scantron sheet in the white area on the back in ink. B. Write and code in the spaces indicated: 1) Name (last name, ﬁrst initial, middle initial)
2) UF ID number 3) Discussion section number C. Under “special codes”, code in the test ID number 4, 2.
1 2 3 e 5 6 ~ 7 8 9' Q
1 e 3 . 4 5 6 7 8 9 0 D. At the top right of your answer sheet, for “Test Form Code” encode B.
A e C D E t ’ E. This test consists of 11 ﬁve—point multiple choice questions, one ﬁvepoint 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 MA02311 homepage after the
exam. if“ 1B Problems 1  11 are worth 5 points each. 1. Evaluate liniqu a. 0
b. 4
c. 1/4
(1. 1 ' ' e. does notexist 2. Find F’(m)'if F(ac) = ff”; dt
 ' a. 1/1113:
b. Inﬂux) c. Ina: d. {ii/(1m)? 1
mlna: e. 3. Find if = 9311 an'd’ f(1)'4== 3 (I: 4. Evaluate limmao a;("’2).
a. 0 ’b.e c. e2 (1.1 e. +00,  5. Find a and b so that
» b. ‘ 10 v 20 '
/ f(a3)da:—— f(;v)da:= ‘f(a;)daz
a ‘ 20 1 auazz" ‘ 6:20 b.‘a=20 b=1_ c.a=1 =1)le d.a=10 b=20 e.a=10 b==1 6. Use the midpoint rule to compute R4 for the deﬁnite integral 5 .
v /\/2:c—~1d:c
. 1
a?
.b. ~3—
c. \/3—‘+\/5+\/—7‘+3 d.x/§+2+«/6+x/§
e’.1+\/§+\/5~+\/7 7 .v The velocity of' a bob mOVing along the :c—axis on a, spring varies with
time accOrding to the equation v(t) '= lOt ~ 31:2 —— 10 At t = 1, the position of the bob is 20. Which of P, Q and R is true?
P: 3(4) 2 2 . Q: 3(0) : 26 R: 3(2) 2 18 ‘
a. Only P and Q are true
b. Only P is true
0. OnlyP and R are true
(1. Only Q and R are true
6. All are true 8. Let A be the area bounded by f = ewz) 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. 05143462
'b.4‘_<.A£4e9'
Lang/13439
d. 0394916 e. 4e£AS4e2 3 9. Find 3% cos(7rt2)' dt
a. 351:2 cos(7rar:3)
b.’ 33:2 cos_(7rm6) —— cos(7rx2)
c. cos(7rzz:6) : cos(7rm2)
d. 4— Sin(7ra:6) + sin(7ra:2) e. sin(7rzc6) '—— sin(zrw2) T
. 10. Evaluate 12'1m33_,+00 miffm > a. 2 ’ b. 1/2 ' I 1 d
c. 0 ‘ '
d. 1 e. 1n2‘ 11. Find the area bounded by a: 2 —1, a: = 7r/4 and the x—axis. __ 3e02m ifmZO
f(m)—{1m2 ifas<0 NIH I §+ln
.1.
3 WHO a.
_ b.
' 1
C. In :9: "
i
d. 3
e. does not exist 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 ac and
y should be used? a.m=75 2150
b.513=150 y=100
(3.33:50, y=300
d.m:200 y=300 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
6 inches by 6 inches, and then the sides are to be folded up to create an
open b.ox.What size square (dimension 3: by 3:) should be cut to mazimize
the volume of the box? ‘ Function to be maximized ‘ (1:: ~ 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 = 532/2 .—— 111(m). Complete the following: a) f’($) b) f has a relative at 0) f”($)
d) m) is concave up on
e) 1im$__)0+ fan) 2 ,
011%.”? m) 4—: g) Sketch the‘ graph of f 3. A particle, initially at rest, moves along the {Io—axis such that its accelera
ation at time t > 0 is given by a(t) = cos(t). At the time t = 0, its position
is a: 2: 1. a) Find the velocity function. m) = b) Find the position function. 5(t) = C) Find two values Where the particle is not moving. 4. Use the deﬁnitien Of the deﬁnite integral to compute [02 (3:1: + 1) dm. Some formulas: 22:1 k = 1733421 22:1 k2 = n§n+1)6(2n+1) ’ ' The integrand f is
A21: :2
Using right hand endpoints at; 2 'Compute limnnoo Rn = ...
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