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Unformatted text preview: MAC 2311 w FINAL EXAM
FALL 2007  A. Sign your scentron sheet in ink in the white area. on the back.
B. Write end encode in the spaces indicated: 1) Your name (last name, ﬁrst initial, middle initial)
2) Your UF 1]) number 3) Your discussion section number 0. Underi‘gpecial Codes”, encode the test number 5,1 . D. At the: top right of your scantron sheet, for “Test Form Code”, encode A‘ .‘3BGDE :
i E. This test consists of 23 ﬁvepoint multiple choice questions and 2 fivepoint bonus
multiple choice questions. The time allowed is 120 minutes. F. YOU ARE FINISHED: 1') Before you turn in your test, check carefuﬂy for transcribing errors. Your
responses cannot be changed after you turn in your exam. 2) You must turn in your scantron to the proctor, but you can keep the exam
questions. i J
a
i Note: Problems 1—25 are worth five points each. 1. Find the slope of the tangent line to the graph of f (cc) : 4(33 w» M55)? at the
. point with mcoordinategtl. ‘A4 E6 08 010 Km E
r 2. Which shape below best characterizes the graph of Mac) 2 937 —— x5 — 2:4 near
the point P on the curve where's: 2 1 ? , ‘ f
r ‘ P P ‘J
A. \\ B. r C. {/4 D. L E. none of these i 1 82m m 53;
3. Evaluate the limit: lim ewe—“~—
m~>0 e3” "— :L' m 6”“ AA 3 1 CHIP—4
,5».
Gilt—I E
2 4. Calculate the exact areaijon [—1,1] bounded by the 3:»axis and the curve 1
1‘
‘ 1 $2419” 3350
HQ“
1 1+\/E m>0 Aﬁ asmé Ce+1 Dew2 Eéme ' 1 5. The equation my — Zﬁ m 2 la(y) deﬁnes y implicitly as a function of 23. What
is the slope of the tangent Zine to the curve at the point (4, 1 ) ? ' ‘ A. m s. g c 1:). 00101
E75
sole: 1
f6 6. A rocket érises upward from the ground (initial height zero) with acceleration
given by a(t) : 60': III/82, after t seconds have elapsed. If its velocity is a
recorded: as 200 m/ s after one second has elaysed, what is the height of the
rocket above the ground at that time? 1 A.120tn 13.140111 C. 16011: D. 180 m E. 200m F ’7. Evaluateéthe definite integral: [4 seo2(6) 1311209) d9
L Q (3 8. To adﬁeve a special effect, an elevator that is ascending at 10 ft / sec is filmed I
by a cameraman that is moving away along the horizontal at 2 ft/ sec. At what rate is the slope at of the dotted line (pictured beiow) changing when meioeianay=2sfti2§
1 t E elevator
A. 0.2 visits/sec 1340.8 units / sec I B. 0.4 uhits/sec E. unit/sec ‘ C. 0.6 units/sec l
a: 9.. Evaluate the limit: 11m [2m ~ 322} . 53—40 i 1 i 1 B. 2 C. e D. 32 E. U i ! 16. A spherieal cloud of gas is observed in space. Use differentials to estimate
the erroriin using a measurement of 3 miles for the radius to calculate the volume df the cloud, if the measurement may be off by % mile. A. Qtr 1113.3 B. 12w Em? C. 18w 11113 ' D. 367: me E. 54% mi3  , 11. The height (in feet) of the water at a particular dam is represented by the
continuous function L(m) : 3(m2 _ s + 10", where x is the number of weeks
that have elapsed from the present. Find the value of M + m where M and m are the maximum and minimum height of the water respectively over the
next twogweeks. gem 13.5ft cse om see 12. For the shaded region, is known that the length of s is a function of m given by s = A 1 /1 ~i % dt. Find the rate of change of the perimeter of theshaded
region respect to miwhen a: = 1, if the iengths are measured in meters. A. x/ﬁ {mz/m 2—? mg/m
: 5
3.2+ﬁm2/m E 3—dgm2/m lnlxl 13. What are the vertical asymptotes of the graph of f (m) m ? :1: — 1
;
A.m=:00nly B.m=0anda:=1
C. ct: = 1 only I). there are none
. 3
14. Classﬁy the local‘extrezna of the function 9(a) m a; 4 .
A. no relative maximuim B. one relative maximum
one relative no relative minimum
E
‘ E
C. one relative maximum D. one relative maxima
one relative nainimaj {we relative minimum 15. Evaluate the following limit of Riemann Sums by writing it as a deﬁnite I
integral. 11m ::(n)(li ~ n) n»—>oo I
2:1 I
!
I
.
i
l P”
awe: 7
B. E3— C. m I). {D
CAMEO ' l
g l ,
16. Calculate the exact area square units) bounded by the maxis and the graph
of the" function ﬁx) = 8 on the interval [ 1, 4] . Warning! This function a
is both negative and pofsitive on the interval. ' E B. E. 2 O
pade
53
tot—4 !
l
1
i
l
.
»
l
I
z 17. A particle in a magnetic field travels in a straight line. The force (in Newtons)
acting upon it is given by the function F m \/§ + 32, Where s is the position '
of the particle in meters. At what rate is the force changing with respect to
me when the particle at position 3 = 1 and has velocity 4 m/s. 'A.GN/sec : 8.6N/sec C.8N/sec D. 10 N/sec H.12N/sec 18. Use Newton’s method With the first approximation :61 m 1 to find the third
approximation 223 of thefroot of the function f(22) = 3:3 — m — 1. 5 11
.A. 5 Bi. —— c. mioo
.U phix!
to tote: 6 19. The rateof honey output from a beehive at any given instant is given by
1' 1 : _
w(t) = 100 + (1 Easy mﬂljliters per week, where t is the number of weeks
that have passed from the present time. What is the net amount of honey
produced over the firSt four weeks? F i
1 I E ,
A. 360 IhL B. 400 lmL c. 440 mL D. 480 mL E. 520 mi. 20. Find thejmcoordinate ojf the point on the curve y = v1 + 2x? located at the
shortest gistance from the point (2, 0 ). D.\/§ E.2 75>
NJth
335
(JOIN
('3
5...: 2.1. Evaluate W(1) if itis known that 3?; = 8w(m2 "— 1)% and W(O) m 2.
A.1 3.2 (3.0. A D.—2 3—1 22. Detennine the vaiue of the constant c that makes this piecewisedefined
function continuous: F ix! m<0 Iii{~33
em+c_ 3:30
3g
A} E32 (3.0 13—2 E~1 23. Suppose that the blood sugar level of a certain individual is modeled by
L(t) : 100 +' 4015 — 153 points, where t is the number of minutes that have ,
elapsed after eating. Find the rate at which the blood sugar level is changing _
after 5 minutes, and the average rate of change over the ﬁveminute interval. ‘ _ a
1 l
A. instantaneous rate: 1«35 points per min; average rate: 15 points per min t
[ C. instantaneous rate: f3?) points per min; average rate: 35 points per min
E f B. instantaneous rate: points per min; average rate: 75 points per D. instantaneous rate: #15 points per min; average rate: 35 points per'min E. instantaneous rate: 4—15 points per min; average rate: 15 points per min
i i t BonuSIKS pts each) 1 18m _
24. Evaluate f0 (:6 + as (ice.
9 5 3 ' 1 1
A. ~8 é C. E D. 1 E. i B.
l 25. Of the graphs of the fumiitions listed below, which have both of the horizontal
asymptotes y 2 $1 ? ' 1 — em  a: 2
I. ﬁx) w 1 + em 119(22): m HI. Mrs) : 2; arctan(x)
!
i
A. only B. II only C. I and III only D. II and III only E. I, II, and III YOU HAVE REACHED
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 Spring '08
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 Calculus, Derivative, instantaneous rate, Blood sugar, average rate

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