Spring 08 - ‘ MAC 2311 TEST 3A SPRING 2008 ' ‘ A. Sign...

Info iconThis preview shows pages 1–20. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 4
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 6
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 8
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 10
Background image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 12
Background image of page 13

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 14
Background image of page 15

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 16
Background image of page 17

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 18
Background image of page 19

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 20
This is the end of the preview. Sign up to access the rest of the document.

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 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. 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 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 MA02311 homepage after the exam. a: r rarer 1B Problems 1 - 11 ai'e Hui-forth 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 + $2) a. :l:2 b. O,:l:1 c. O'only d. :tl only e. f has no inflection points 3. Suppose that f’(a:) = 4502(5): — 9) and f”(a:) :, 125122 - 72m. Which of the following isare true? ' P: ACCOrding to the Second Derivative Test, f(:c) has a local minimum at a: = 6 and a local maximum at :3 = O. ' Q: is increasing on (—00,.0) U (9,00) R: f is beth increasing and concave up on (9, 00) a. Q and b. R only c. Q only (:1. P, Q and R e. P and Q only 4. Find threalinearization of f z 3595 - e4‘” near a: = 0. a. y=~§m+l b. yz—ém-l oyzém—l d. y=-§zc+1 e. y=~%m—1 5. Find all the values 0 guaranteed by the Mean Value Theorem for f(:n) = 332 + 651: on [—1,2]. a. c==1~andc=~2 b. c=0andc=1/2 C. czlonly d. c=30nly e. czl/Zonly 6. Find the critical number(s) c for f 2 12:05 ~— 45224 + 402133 at which f(c) is NOT a relative maXimum or relative minimum. * a. 0 and 2 only b. O and 1 only . C. 0 only d. 1 only e. 2 only 7. A particle moves according to the law of motion 5 = te‘t/2 Where s is in feet and t is in seconds. When is the particle moving in a positive direction? a.0<t<1/2. b. 1<t<2 c.1/2<t<oo d.0<t<2 e.2<t<oo 8. The area of a circle is expanding at a constant rate of 16 square inches. per second. How fast is the circumference of the circle increasing when the radius is 4 inches? a. 1 in/sec b. 2 in/sec c. 3 in/sec d. 4 in/sec e. 5 in/sec 9. Use differentials to approximate the value of x/ 16.328. a. 4.082 b. 4.042 c. 4.041 d. 4.0328 e. 4.164 10. A 25 foot ladder rests against a vertical wall. If the bottom of the ladder is pulled away from the wall at 5 ft / sec, how fast is the top of the ladder falling at the instant when the top is 20 ft above the ground? a. 5/2 ft/sec b. —5/4 ft/sec c. —15/4 ft/sec d. —15/8 ft/sec e. 5/4 ft/sec 11. Find the differential dy‘for the function f z ” 14—25:: a. (112%? b- at“; C' 14:1ng (1' (14%;)2 3' (1.13:)2 12. (Bonus!) Given the graph of the derivative f ’ (:23), which of the following statements is / are true of the graph of P: f($) 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. ...
View Full Document

This note was uploaded on 02/10/2011 for the course MAC 2311 taught by Professor All during the Spring '08 term at University of Florida.

Page1 / 20

Spring 08 - ‘ MAC 2311 TEST 3A SPRING 2008 ' ‘ A. Sign...

This preview shows document pages 1 - 20. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online