# Register now to access 7 million high quality study materials (What's Course Hero?) Course Hero is the premier provider of high quality online educational resources. With millions of study documents, online tutors, digital flashcards and free courseware, Course Hero is helping students learn more efficiently and effectively. Whether you're interested in exploring new subjects or mastering key topics for your next exam, Course Hero has the tools you need to achieve your goals.

2 Pages

### f-F01-S01

Course: MATH 131, Fall 2008
School: UMass (Amherst)
Rating:

Word Count: 600

#### Document Preview

131: Mathematics Final, May 22, 2001 1) Consider the function -t2 + 2t + 1, h(t) = t2kt , 2+1 t - 2t + 3, t -1 -1 &lt; t &lt; 1 t 1. A. Find the value of k that makes h(t) a continuous function. Explain! B. Is h(t) (with this value of k) differentiable at t = 1? Explain! 2) Let f (x) = A. Evaluate limx f (x). B. What is the horizontal asymptote to the graph of f (x)? 3. A waterskier skis over a...

Register Now

#### Unformatted Document Excerpt

Coursehero >> Massachusetts >> UMass (Amherst) >> MATH 131

Course Hero has millions of student submitted documents similar to the one
below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support.

Course Hero has millions of student submitted documents similar to the one below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support.
131: Mathematics Final, May 22, 2001 1) Consider the function -t2 + 2t + 1, h(t) = t2kt , 2+1 t - 2t + 3, t -1 -1 < t < 1 t 1. A. Find the value of k that makes h(t) a continuous function. Explain! B. Is h(t) (with this value of k) differentiable at t = 1? Explain! 2) Let f (x) = A. Evaluate limx f (x). B. What is the horizontal asymptote to the graph of f (x)? 3. A waterskier skis over a straight ramp. Her speed is 13 m/s in the direction of the slope of the ramp (i.e., not horizontally). If the ramp is 12m long and 5m high, how fast is she rising when she leaves the ramp? 4. Use L'Hopital's Rule to find the value of the limit x0 7x2 + 4x . 2x2 - x + 3 lim (1 + xex )1/ sin(x) 5. For the function f (x) = x4 - 8x2 , find A. The intervals where the function is increasing and decreasing. B. All local maxima and minima C. The intervals on which the function is concave up and down, and its inflection points. D. Sketch the graph, clearly indicating these points and intervals. 6. Consider the function f (x) = (x2 - 4x + 3)2/3 defined on the closed interval 0 x 5. A. Find all critical points of f (x) on the interval 0 x 5. B. Find the global (absolute) minimum and global (absolute) maximum of f (x) on this interval. 7. A square piece of tin 18 cm on a side is to be made into a rectangular box without a top by cutting a square from each corner and then folding up the flaps to form the sides. What size corners should be cut in order that the volume of the box be as large as possible? Mathematics 131: Final, December 19, 2001 1) Consider the function x2 + x + k, x 0 f (x) = kex , 0<x<1 x kex, 1. A. Show that f (x) is continuous for all values of k. B. Determine the value of k so that the function f (x) is differentiable for all x. 2) Find the points on the ellipse 2x2 + y 2 = 1 where the tangent line has slope 1. 3) If a (perfectly round) snowball melts so that its surface area decreases at a rate of 2 cm2 /min, find the rate at which the diameter decreases when the diameter is 5 cm. (Hint: surface area A of a ball A = 4r2 where r is the radius of the ball.) 4) Find the following limits A. limx0 5+x- 5 x B. limx0 [1 + sin(2x)]1/x 5) Consider the function f (x) = x3 - 6x2 + 9x - 3 defined on the interval [0, 4]. A. Find the critical points of f (x) on [0, 4] and decide if the critical points are local maxima or minima. B. Find the absolute maximum and minimum values of f (x) on [0, 4]. C. Determine the intervals in the domain of f (x) on which f (x) is concave up. 6) Let g(x) = (x2 + 2x - 2)e-x be defined on the interval [-3, 4] A. The g...

Find millions of documents on Course Hero - Study Guides, Lecture Notes, Reference Materials, Practice Exams and more. Course Hero has millions of course specific materials providing students with the best way to expand their education.

Below is a small sample set of documents:

UMass (Amherst) - MATH - 131
DEPARTMENT OF MATHEMATICS AND STATISTICS UNIVERSITY OF MASSACHUSETTS MATH 131 Spring 2004 EXAM #2Your Section Number:Your Instructors Name:Print Your Name:Sign Your Name:This exam consists of 5 questions. It has 5 numbered pages. On this exam, you ma
UMass (Amherst) - MATH - 131
DEPARTMENT OF MATHEMATICS AND STATISTICS UNIVERSITY OF MASSACHUSETTS EXAM 2: MATH 131 Spring 2003 30 April 2003Your Name: Your Instructors Name: This exam paper consists of 9 questions. The value of each question is as indicated. It has 8 pages, includin
UMass (Amherst) - MATH - 131
DEPARTMENT OF MATHEMATICS AND STATISTICS UNIVERSITY OF MASSACHUSETTS MATH 131 Fall 2003 EXAM #2 Your Section Number:Your Instructors Name:Print Your Name:Sign Your Name:This exam consists of 7 questions. It has 8 numbered pages, where the last is a bl
UMass (Amherst) - MATH - 131
DEPARTMENT OF MATHEMATICS AND STATISTICS UNIVERSITY OF MASSACHUSETTS MATH 131 Fall 2002 EXAM 2Your Name:Your Instructors Name:This exam paper consists of 7 questions. It has 9 pages. On this exam, you may use a calculator, but no books or notes. It is
UMass (Amherst) - MATH - 131
Mathematics 131: 2nd midterm, April 26, 20011) A squash ball is hit upwards so that its height in meters is given by h(t) = 5t - 10t2 , where t is the elapsed time in seconds. A. (10 pts) Find the velocity after 0.1 sec, 0.2 sec and 0.3 sec, respectively
UMass (Amherst) - MATH - 131
DEPARTMENT OF MATHEMATICS AND STATISTICS UNIVERSITY OF MASSACHUSETTS MATH 131 Spring 2004 DERIVATIVES EXAM Your Section Number: Your Instructors Name: Print Your Name: Your ID Number: Sign Your Name: For each function y = f (x) given below, compute dy/dx.
UMass (Amherst) - MATH - 131
DEPARTMENT OF MATHEMATICS AND STATISTICS UNIVERSITY OF MASSACHUSETTS MATH 131 Fall 2003 DERIVATIVE TESTYour Section Number:Your Instructors Name:Print Your Name:Sign Your Name:This exam consists of 7 questions. It has 2 numbered pages, where the last
UMass (Amherst) - MATH - 131
DEPARTMENT OF MATHEMATICS AND STATISTICS UNIVERSITY OF MASSACHUSETTS Math 131 Spring 2003 Derivative Test Wednesday April 9 Your Name: Your Instructor's Name: Your Section Number: Find the derivative of each of the following functions of the variable x. D
UMass (Amherst) - MATH - 131
UMass (Amherst) - MATH - 131
UMass (Amherst) - MATH - 131
MATH131 Calculus I Derivative Exam Practice ProblemsPractice Exam #1 (10 points per question): 3x8 + 8 x -1 - 6 x -9 - 7 = 1) d dx 2) d 3) d 4) d 5) d 6) d 7) d 8) d 9) d 10) ddx dt ds sin( x) + tan( x) = 7sec(t ) - 2 t =(-8s -15 - 2) cot( s ) =cot( s
UMass (Amherst) - MATH - 131
DEPARTMENT OF MATHEMATICS AND STATISTICS UNIVERSITY OF MASSACHUSETTS MATH 131 Spring 2004 EXAM I Your Section Number:Your Instructors Name:Print Your Name:Your ID Number:Sign Your Name:This exam consists of 5 questions. It has 6 numbered pages, where
UMass (Amherst) - MATH - 131
DEPARTMENT OF MATHEMATICS AND STATISTICS UNIVERSITY OF MASSACHUSETTS MATH 131 Fall 2003 EXAM #1 Your Section Number:Your Instructor's Name:Print Your Name:Sign Your Name:This exam consists of 7 questions. It has 8 numbered pages, where the last is a b
UMass (Amherst) - MATH - 131
DEPARTMENT OF MATHEMATICS AND STATISTICS UNIVERSITY OF MASSACHUSETTS MATH 131 Fall 2002 EXAM 1Your Name:Your Instructors Name:This exam paper consists of 7 questions. It has 9 pages, where the last is a blank page. On this exam, you may use a calculato
UMass (Amherst) - MATH - 131
DEPARTMENT OF MATHEMATICS AND STATISTICS UNIVERSITY OF MASSACHUSETTS EXAM 1: MATH 131 Spring 2003 12 March 2003Your Name: Your Instructor's Name: This exam paper consists of 10 questions, all of equal weight. It has 9 pages. On this exam, you may use a c
UMass (Amherst) - MATH - 131
Fall '01 - Exam 1(1) (15 pts) (a) The following is a table of values for the function f (x) = 2x/(x2 + 1). Compute the slopes of the secant lines through each of these points and the point (0, 0). Use your table to estimate the slope of the tangent line
UMass (Amherst) - MATH - 131
2Spring 01 - Exam 1(1) (10 pts) Evaluate the limitx1lim1x 1 xshowing all your steps clearly. (2) (10 pts) Calculate the derivative f (x) of the function f (x) = 1/x2 directly from the denition. (3) (10 pts) You are given the function (1 2x)(1 x) g(x
Texas A&M - M - 151
M151B Practice Problems for Final ExamCalculators will not be allowed on the exam. Unjustified answers will not receive credit. On the exam you will be given the following identities: n(n + 1) ; k= 2 k=1nn(n + 1)(2n + 1) k = ; 6 k=12nnk3 =k=1n(n
Texas A&M - M - 151
Additional problems, due Tuesday Nov. 181. Use the method of Riemann sums to compute2 1x2 dx.2. Use the method of Riemann sums to compute1 0x3 dx.3. Use the method of Riemann sums to compute1 0ex dx.Hint 1. Use the following summation formula: f
Texas A&M - M - 151
M151B, Fall 2008, Practice Problems for Exam 2Calculators will not be allowed on the exam. 1. Let f (x) = cos x - sin x, and compute 2. Show thatdf -1 (1). dx-3 x , 4 41 d cos-1 x = - , dx 1 - x2 y = xtan x ,-1 &lt; x &lt; +1. , 23. Let 0x&lt; and computed
Texas A&M - M - 151
M151B Practice Problems for Exam 1Calculators will not be allowed on the exam. Unjustified answers will not receive credit. 1. Compute each of the following limits: 1a. x2 - 4 . x2 x - 2 limx31b. lim - x2x . - 2x - 3 sin 7x . x1c.x0lim1d.x1lim
Texas A&M - M - 151
MATLAB for M151Bc 2008 Peter Howard1MATLAB for M151BP. Howard Fall 2008Contents1 Introduction 1.1 The Origin of MATLAB . . . . . . . . . . . . 1.2 Our Course Goal . . . . . . . . . . . . . . . . 1.3 Starting MATLAB at Texas A&amp;M University 1.4 The MA
Texas A&M - M - 151
Additional ProblemsThe following problems were taken from Calculus: Early Vectors, by J. Stewart, which is being used by the other sections of M151. 1. A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the wa
Boise State - CS - 253
COMPSCI 297: Object-Oriented Program Development in CAmit Jain 426-3821 amit@cs.boisestate.edu http:/cs.boisestate.edu/amitCatalog DescriptionIntroduction to object-oriented style of programming in C for Java programmers in a Linux/Unix environment. Ba
University of Toronto - MATH - 477
Polar Factorization and Monotone Rearrangement of Vector-Valued FunctionsYANN BRENIERUniversite` de Paris VIAbstract Given a probability space ( X , p ) and a bounded domain R in R d equipped with the Lebesgue measure 1 . I (normalized so that 10I = I
University of Toronto - MATH - 477
An Inequality for Rearrangements G. G. Lorentz The American Mathematical Monthly, Vol. 60, No. 3. (Mar., 1953), pp. 176-179.Stable URL: http:/links.jstor.org/sici?sici=0002-9890%28195303%2960%3A3%3C176%3AAIFR%3E2.0.CO%3B2-Y The American Mathematical Mont
University of Toronto - MATH - 477
MAT 477H Fall Semester Syllabus 2007-08 (revised) PRIMARY SOURCES Weeks 1 Introduction and Historical Overview of Optimal Transportation [4]. 2 Continue Orientation [5]. Finish deciding who presents what. 3 L. Kantorovich. On the translocation of masses.
University of Toronto - MATH - 477
University of Toronto - MATH - 477
ARTICLE IN PRESSAdvances in Mathematics 182 (2004) 307332http:/www.elsevier.com/locate/aimA mass-transportation approach to sharp Sobolev and GagliardoNirenberg inequalitiesD. Cordero-Erausquin,a, B. Nazaret,b and C. Villanibamatiques Applique (CNRS
University of Toronto - MATH - 477
Journal of Mathematical Sciences, Vol. 133, No. 4, 2006ON THE TRANSLOCATION OF MASSES L. V. KantorovichThe original paper was published in Dokl. Akad. Nauk SSSR, 37, No. 78, 227229 (1942).We assume that R is a compact metric space, though some of the d
University of Toronto - MATH - 477
PACIFIC JOURNAL OF MATHEMATICS Vol. 17, No. 3, 1966CHARACTERIZATION OF THE SUBDIFFERENTIALS OF CONVEX FUNCTIONSR. T. ROCKAFELLAREach lower semi-continuous proper convex function / on a Banach space E defines a certain multivalued mapping df from E to E
University of Toronto - MATH - 477
Mathematics 477Y Professor Robert McCann www.math.toronto.edu/mccann/477.html STUDENT SEMINAR ON VARIATIONAL PROBLEMS IN PHYSICS, ECONOMICS, AND GEOMETRY Current Lecture Hours: Thursday 16h10-18h00 BA 6183 (guest lecturer Oct 25) Oce Hours: Thursday 18h05
East Los Angeles College - CONLL - 114
Introduction to the CoNLL-2004 Shared Task: Semantic Role LabelingXavier Carreras and Llus M` rquez a TALP Research Centre Technical University of Catalonia (UPC) cfw_carreras,lluism@lsi.upc.esAbstractIn this paper we describe the CoNLL-2004 shared tas
Oregon State University - PH - 203
PH 203H/213H S09Homework due May 14, 20091. A 2.00-m long pole is mounted vertically in a swimming pool. The top of the pole extends 0.50 m above the surface of the water. Light from the sun, which is 55 above the horizon, shines on the pole. What is th
Oregon State University - PH - 203
PH 203H/213H S09Homework due Monday, May 4, 20091. The square loop of wire of side b = 0.16 m lies on a long straight wire with a = 0.12 m on one side of the wire and b a = 0.04 m on the other side. The current in the long wire is I = 4.50t2 10.0t, wher
Oregon State University - PH - 203
PH 203H/213H S09Homework due Thursday May 7, 20091. An electric field of a plane electromagnetic wave propagating in the +z direction is given by Ex = 0, E y = E0 sin(kz ! &quot; t) , Ez = 0, with E0 = 2.34 10-4 V/m and k = 9.72 106 m-1. (a) Find the 3 compo
Oregon State University - PH - 203
PH 203H/213H S09Homework due Thursday, April 301. A circular coil of wire of radius 5.2 cm lies in the plane of the page. The resistance of the coil is 0.21 . Pointing out of the page is a magnetic field that is perpendicular to the plane of the loop an
Oregon State University - PH - 203
PH 203H213H S09Homework due Tuesday April 29, 20091. An alpha particle (Q = +2e, m = 4.00 u) travels in a circular path of radius 4.50 cm in a uniform magnetic field of strength 1.20 T. Calculate (a) its speed, (b) its period of revolution, (c) its kine
Oregon State University - PH - 203
PH 203H/213H W09Homework due April 23, 2009Chapter 20: problems 27, 28, 48, and 49 Answers: 27. 1.1 x 10-11 N
Oregon State University - PH - 203
PH203H/213H S09Homework due Thursday April 16, 20091. A parallel-plate capacitor has circular plates of 8.2 cm radius and 1.3 mm separation. (a) Calculate the capacitance. (b) What charge will appear on the plates if they are connected across a 12-volt
Oregon State University - PH - 203
PH203H213H S09Homework due Monday, April 13 @ 5:00 pm1. Calculate the average time between collisions and the average number of atoms passed between collisions for electrons in aluminum. Aluminum has an effective valence of 3 (meaning 3 electrons per at
Oregon State University - PH - 203
PH203H/213H W09Homework due April 9, 2009Chapter 18: problems 45 and 46 Answers: 45. c) 2_ N/C 46. d) 4_ N/C
Oregon State University - PH - 203
Ph203H/213H W09Homework due April 6, 2009 5:00pmChapter 17: problems 45, 49, 50, and 55 Answers: 50. b) 0.49 Am2
Oregon - ECON - 201
Grade Distributions Midterm 1 A 40&amp;UP A39 B+ 38 B 32-37 B31 C+ 30 C 25-29 C22-24 D 20-21 F 0-19 Mean Std. Dev. 30.61 6.63Midterm 2 40&amp;UP 39 38 32-37 31 30 25-29 22-24 20-21 0-19 30.02 7.9
Oregon - ECON - 101
Grade A AB+ B BC+ C CD F mean std. dev.Distribution: Midterm 1 + 4 45 &amp; UP 44 43 39-42 38 37 31-36 29-30 28 BELOW 28 37.22 7.2Distribution: Midterm 2 + 4 45 &amp; UP 44 43 39-42 38 37 30-36 28-29 26-27 BELOW 25 32.99 6.3
UConn - MATH - 105
Exam 2 GuideMathematics 105QMarch 2007The examination will cover the topics dealt with in Sections 2.1-2.6 and 3.1-3.2 in our textbook. So students will need to be prepared on the use of row operations to solve systems of linear equations systematicall
Gardner-Webb - G - 103
@?@?@ f@? ?@?@?eh?@? ? ?@?@?@?@?e?@?h?@? ? ?@?@?f?@?e@?eh?@? ? ?@?f?@?e?@?@?@?f?@?e?@?@?f?@Be&lt;@?@Be&lt;@?h?@? h?@?g?@?e?@?e?@?f?@?e?@?@?@?f?@?e?@?@?@?=@C?@?=@C?@?f?@? h?@?g?@?e&lt;@Be?@?f?@?e?@?@?@?f?@?e?@?@?@?@?@?@?@?f&lt;@? h?@?g?@?@?@?@?f?@?e?@?@?@?f?@?e?@?@?f?
UConn - MATH - 105
Review Problems for Exam 1 1. In a certain bank interest is 6% per year compounded quarterly. a. How much will \$1000 today be worth in 10 years? b. How much must be deposited today so that it will accumulate to \$1000 in 10 years? 2. At the end of every 3
National Taiwan University - CSE - 200
A B C D 1 TRAVEL PACKAGE INFORMATION 2 # people in family 3 family 4 Smith 4 5 Adams 5 6 Reeves 3 7 Williams 6 8 Johnson 5 9 Jones 5 10 11EFGH PER PERSONI travel allowance amount \$1,500.00 \$800.00 \$1,000.00 \$300.00 \$400.00 \$1,800.00city Tokyo Santia
National Taiwan University - CSE - 200
1 2 3 4A test dates test number how many percentageB 3-Jan 1 1 16.7%C D 2-Feb 4-Mar 2 3 2 1 33.3% 16.7%E 3-Apr 4 0 0.0%F G H I J K L M 3-May 2-Jun 2-Jul 1-Aug 31-Aug 30-Sep 30-Oct 29-Nov 5 6 7 8 9 10 11 12 1 0 1 0 0 0 0 0 16.7% 0.0% 16.7% 0.0% 0.0% 0
National Taiwan University - CSE - 200
A B C D 1 EXCEL-LENT CAR BUYING DEALERSHIP 2 3 # cars 7 4 5 6 7 8 9 10 11 12 13 14 15 16 car Mustang Thunderbird Escape F150 Sienna Highlander Accord company type of car ford sport ford sport ford suv ford truck toyota van toyota suv honda sedan sticker \$
National Taiwan University - CSE - 200
1 2 3 4 5 6 7 8 9 10 11 12 13 14A B C D E F G H I J K L M N TRIATHLON TRAINING below avg on total time t-shirt time in minutes average mph name gender swim bike run all events in hrs place compete level swim bike run cost Abby F 10 55 20 FALSE 1.4 3 TRUE
National Taiwan University - CSE - 200
A 1 2 3BCDEFGHITHEME PARK VACATION TRAVELticket type # days senior 5 child 5 regular 11 child 11 child 11 regular 1 senior 7 regular 7 hotel ticket \$/ night discount \$ 200.00 15% \$ 150.00 25% \$ 100.00 0% \$ 250.00 25% \$ 50.00 25% \$ 100.00 0% \$ 50
National Taiwan University - CSE - 200
A 1 2 3 4 5 6 7 8 9 10 11 12 13 14BCEXCEL PAINTBALL TOURNAMENTPLAYER TEAM# level Dave 1 3 Jim 2 3 Bryan 3 5 Zach 2 1 Kelly 3 4 Taylor 4 3 S ydney 3 3 Jeff 1 3 Cliff 1 4 Daniel 2 3 Nicole 3 4 Rick 4 2A B C D E F G H I J K 1 FYI: the tournament actuall
National Taiwan University - CSE - 200
acct# acctype ssn lname fname 456 A 123456789 Sommer Martn 543 B 139555002 Suyama Michael 544 A 157745969 Lebihan Laurence 999 A 123456789 Sommer Martn 1112 C 178301771 Berglund Christina 2456 B 201529842 Trujillo Ana 3575 C 257436001 Citeaux Frdrique 678
University of Toronto - STA - 247
HPH !U!czPP0PxPPPU7cg rr5cPuUPscuvvggoc2cSrzvugcPPvcg PP7PPgPP7P cSS c PPgPP7PPg P c 7PPgPP7PPg UcPu0PcUgWPvcr2ugc PPec PPgPP7PPgPP 7PducPc2cSrF r7g 2uFg
University of Toronto - STA - 247
%!PS-Adobe-2.0 %Creator: dvips(k) 5.92b Copyright 2002 Radical Eye Software %Title: test-sol.dvi %Pages: 4 %PageOrder: Ascend %BoundingBox: 0 0 612 792 %DocumentFonts: CMR12 CMBX12 CMMI12 CMTI12 CMSY10 CMR8 CMBXTI10 CMEX10 %EndComments %DVIPSWebPage: (www
University of Toronto - STA - 247
STA 247, Fall 2003 Solutions to the Mid-term Test1. Every year you cook a turkey and a ham for Thanksgiving dinner. You also invite four of your friends over to help eat the turkey and the ham. You have ten friends altogether. Four of your friends like t
University of Toronto - STA - 247
%!PS-Adobe-2.0 %Creator: dvips(k) 5.92b Copyright 2002 Radical Eye Software %Title: old-mid-sol.dvi %Pages: 3 %PageOrder: Ascend %BoundingBox: 0 0 612 792 %DocumentFonts: CMR12 CMTI12 CMEX10 CMMI12 CMSY10 CMMI8 CMR8 %EndComments %DVIPSWebPage: (www.radica