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Unformatted text preview: ‘ MAC 2311 TEST 3A SPRING 2008 ' ‘ A. Sign your scantron sheet in the white area on the back in ink. B. Write and code in thespaces 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 3, 1.
1 '2 o 4 5 6 7 8 9 0
a 2 3 4 5 6 7 8 9 0 I 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 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. I 3) The answers will be posted on the MACZ311 homepage after the
exam. ' 1A Problems 1 — 11 are" worth Sipoints each. 1. Find the maximum and minimum values of. f :3 \3/ 2:1:  m2 on [—2, 2]
‘ a. maximum: 0 minimum: —2
b. maximum: 1 minimum: 0
c. maximum: none minimum: 0
d. maximum: 1 minimum: —2 e. maximum: none minimum: 1 2. Find all the inﬂection points on the graph of f 2 ln(1 + 332)
a. $1 only
b. 0 only
c. O,i1
d. i2 e. f has no inﬂection points 3. Suppose that f’(a:) 2 4332(95 — 9) and f”(m) = 12902 —— 7200. Which of the
following is / are true? ‘ . , P: Ac'cording to the Second Derivative Test, f has a local minimum at
a: = 6 and a local maximum at m z: 0. Q: is increasing on (~oo,O) U (9, 00) R: is both increasing and concave up on (9,00) a. Q and R b. Q only c. R only d. P, Q and R
e. P and Q only f
f . a t ' {<9 7.
4. Find the linearlzation of f = 5;— — 64”” near a: 2 O. ay=~§x~1 f by=~~§x+1 f
c y=%m~1 d y=——~%az——1 e y=g~a§+1 5. Find all the values 0 guaranteed by the Mean Value Theorem for 2 £132 + 693 on [~1,2]. a. c=1andcz~2
b. c=0andc=1/2
c.c=:10nly d. c=1/2only .e. c: 3 only 6. Find the critical number(s) c for ﬁx) 2 121135 — 45$4‘ + 409:3 at which
f(c) is NOT a relative maximum or relative minimum. a. O and 2 only
1). O and 1 only
c. 2 only d. 1 only
e. 0 only 7. A particle moves according to the law of motion 3 = rte—V2 where s is in
feet and t is in seconds. When is the particle moving in a positive direction? a.0<t<l/2
b.0<t<2
c.1/2<t<oo
d.1<t<2
e.2<t<oo 8. The area of a circle is expanding at a constant rate of 16 square inches
per second. How fast is the circumference of the circle increasing when the
radius is 4 inches? a. 5 in/sec
b. 4 in/sec
c. 3 in/sec
d. 2 in/sec e. 1 in/sec 9. Use differentials to approximate the value of a. 4.042
b. 4.082
c. 4.164
d. 4.0328 e. 4.041 p p 10. A 25 foot ladder rests against a vertical wall. If the bottom of the
ladder is pulled away from the wall at 5 ft / sec, how fast is the top of the
ladder falling at the instant when the top is 20 ft above the ground? a. 5/2 ft/sec b. —5/4 ft/sec _ c. ~15/4 ft/sec d. ~15/8 ft/sec e. 5/4 ft/sec % 11. Find the differential dy for the function f = 9” 1+2m
3' (1433090?
b (1—7—3352
0' 1—3333}?
d ($205532
9' 11%; 12. (Bonus!) Given the graph of the derivative f’ (ac), which of the following
statements is / are true of the graph of ﬂan)? P: is concave upward on (~2, 2).
Q: has a local minimum at m =2 0 and a: = i5.
R: W) > M)
a. P and R only
b. Q only" ,
c. P only
. ‘d. P,QandR’ e. R only MAC 2311 EXAM 1 Part II
Spring 2008 Section Number Name UF ID Number Signature
SHOW ALL WORK TO RECEIVE FULL CREDIT 1. Given 4a: 4502 — 12 me) = ($2 —1)2/3, W) = ‘W 2 has critical numbers at cc 2 v a: is increasing on a: = a: is decreasing on a: = a: has horizontal tangent lines at cc 2 :c has local maximum(s) at a: =
:3 has local minimum(s) at a: :2
a: is concave upward on )
)
)
)
:c) has vertical tangent lines or cusps at (r =
)
)
)
x) is concave downward on
) (
(
(
(
(
(
(
(
(
( xxxxxxxxxx :13 hasinﬂection point(s) at 2. Sketch a graph of f(ac) of the function from Problem 1. Use
all of the information obtained in Problemﬁl. Label all intercepts, local
extrema, and inﬂection points. 3/7 “A” " " ° 5’ 3. The number of bacteria N (t) is modeled by N (t) = 1332 + 3
where N is in thousands of bacteria and t is in minutes. ' I ' ’ a. What was the population of bacteria when the bactericide was ﬁrst
introduced? bacteria b. What is the average rate of change in the number of bacteria during
the ﬁrst three minutes? Provide the correct units with you answer. c. At what rate is the number of bacteria changing at t = 2 minutes?
Provide the correct units with you» answer. d. What is the least number of bacteria that will be present as time
continues? Hint: lirr1t_...>00 N bacteria 4. The line of sight from an observer on one side of University
Avenue makes an angle of 6 with a cyclist headed east on the other side of
University Avenue. If University Avenue is 40 feet Wide and the angle is
increasing at 8 radians per minute, how fast is the cyclist moving When she
is 30 feet east of a point directly across from the observer. ﬂbservcr ' Lin/“yer 537’ ﬁve“ “’5” d0_
dt '— What are we trying to ﬁnd? Equation: The cyclist is moving at ft / min. MAC 2311 TEST 3B
SPRING 2008 A. Sign your scantron sheet in the whitearea 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 3)_ Discussion section number C. Under “special codes”, code in the test ID number 3, 2.
1 2 e 4 5 6 7 8 9 0
1 o 3 4 5 6 7 8 9 0 D. At the top right of your answer sheet, for “Test Form Code” encode B.
A o C E 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. a: r rarer 1B Problems 1  11 ai'e Huiforth 5 points each. 1. Find the maximum and minimum values‘of = 3 :62 — 2:13 on [~2,' 2] a. maximum: —1 minimum: none
b. maximum: minimum: —1 0. maximum: 0 minimum: none .
(1. maximum: —1 minimum: —1 e. maximum: 2 minimum: 0 2. Find all the inﬂection points on the graph of f = ln(1 + $2)
a. :l:2
b. O,:l:1
c. O'only
d. :tl only
e. f has no inﬂection points 3. Suppose that f’(a:) = 4502(5): — 9) and f”(a:) :, 125122  72m. Which of the
following isare true? ' P: ACCOrding to the Second Derivative Test, f(:c) has a local minimum at
a: = 6 and a local maximum at :3 = O. ' Q: is increasing on (—00,.0) U (9,00)
R: f is beth increasing and concave up on (9, 00)
a. Q and b. R only
c. Q only
(:1. P, Q and R
e. P and Q only 4. Find threalinearization of f z 3595  e4‘” near a: = 0. a. y=~§m+l
b. yz—éml oyzém—l d. y=§zc+1
e. y=~%m—1 5. Find all the values 0 guaranteed by the Mean Value Theorem for
f(:n) = 332 + 651: on [—1,2]. a. c==1~andc=~2
b. c=0andc=1/2
C. czlonly d. c=30nly e. czl/Zonly 6. Find the critical number(s) c for f 2 12:05 ~— 45224 + 402133 at which
f(c) is NOT a relative maXimum or relative minimum. * a. 0 and 2 only b. O and 1 only .
C. 0 only
d. 1 only
e. 2 only 7. A particle moves according to the law of motion 5 = te‘t/2 Where s is in
feet and t is in seconds. When is the particle moving in a positive direction? a.0<t<1/2.
b. 1<t<2
c.1/2<t<oo
d.0<t<2
e.2<t<oo 8. The area of a circle is expanding at a constant rate of 16 square inches. per second. How fast is the circumference of the circle increasing when the
radius is 4 inches? a. 1 in/sec
b. 2 in/sec
c. 3 in/sec d. 4 in/sec e. 5 in/sec 9. Use differentials to approximate the value of x/ 16.328.
a. 4.082 b. 4.042
c. 4.041
d. 4.0328
e. 4.164 10. A 25 foot ladder rests against a vertical wall. If the bottom of the
ladder is pulled away from the wall at 5 ft / sec, how fast is the top of the
ladder falling at the instant when the top is 20 ft above the ground? a. 5/2 ft/sec
b. —5/4 ft/sec
c. —15/4 ft/sec
d. —15/8 ft/sec
e. 5/4 ft/sec 11. Find the differential dy‘for the function f z ” 14—25::
a. (112%?
b at“;
C' 14:1ng
(1' (14%;)2
3' (1.13:)2 12. (Bonus!) Given the graph of the derivative f ’ (:23), which of the following
statements is / are true of the graph of P: f($) is concave upward on (—2,2).
Q: f(93) has a local minimum at m = 0 and a: = i5.
R: f (2) > f (4) a. P and R only b. Q only c. P only (1. P, Q and R e. R only MAC 2311 EXAM 1 Part II
Spring 2008 ' Section Number Name
UF ID Number
Signature
SHOW ALL WORK TO RECEIVE FULL CREDIT
1. ' Given —4:U ~4$2 + 12 : _(m2 ‘ 1)2/37 ‘f/(m) : W, fI/(m) = W at: has critical numbers at a: 2
:c is increasing on cc = cc is decreasing on :c = a; has horizontal tangent lines at a: = a: has vertical tangent lines or cusps at a: = H a: has local minimum(s) at :0 =
a: is concave upward on a: is concave downward on xxxxxxkﬁkhxx
AAA/\AAAAAA )
)
)
)
)
) has local maximum(s) at a: =
)
)
)
) as has inﬂection point(s) at 2. Sketch a graph of f(:r) of the function from Problem 1. Use
all of the information obtained in liroblem 1. Label all intercepts, local
extrema, and inﬂection points. z/C/ "at: I» 6‘ 5“ 3. The number of bacteria N (t) is modeled by N (t) = 30 + 2
where N is in thousands of bacteria and t is in minutes. I . a. What was the population of bacteria when the bactericide was ﬁrst
introduced? ' bacteria b. What is the average rate of change in the number of bacteria during
the ﬁrst three minutes? Provide the correct units with you answer. c. At what rate is the number of bacteria changing at t = 2 minutes?
Provide the correct units with you answer. i d. What is the least number of bacteria that will be present as time
continues? Hint: limp.mo N bacteria 4. ’ The line of sight from an observer on one side of University
Avenue makes an angle of 9 with a cyclist headed east on the other side of
University Avenue. If University Avenue is 30 feet Wide and the angle is
increasing at 4 radians per minute, how fast is the cyclist moving when she is 40 feet east of a point directly across from the observer.
Observes/ d6
dt What are we trying to ﬁnd? Equation: The cyclist is moving at ft / min. ...
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 Spring '08
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 Mathematical analysis, Fermat's theorem

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