Quiz 1. Department of Mathematical Sciences Instructor: Markus Schmidmeier Calculus II August 26, 2016
|
|
|
- Delilah Pearson
- 6 years ago
- Views:
Transcription
1 Department of Mathematical Sciences Instructor: Markus Schmidmeier Calculus II August 26, 2016 Name: Quiz 1 1. Consider an object moving long a line with velocity v(t) = 6 2t during the time interval [0, 4]. The initial position is s(0) = 0. (a) Graph the velocity function on the given interval and determine when the object is moving in the positive direction and when it is moving in the negative direction. (b) Determine the position function and graph the position function on the given interval. (c) Determine the displacement and the distance traveled over the given interval. P.T.O.
2 2 Calculus II, Quiz 1, August 26, Consider the functions f(x) = 3 x, g(x) = x (a) Sketch the graphs of the line and the parabola. (b) Find the two intersection points. (c) Find the area between the two graphs. (d) Verify the result in (c) by making a (possibly rough) estimate.
3 Department of Mathematical Sciences Instructor: Markus Schmidmeier Calculus II September 2, 2016 Name: Quiz 2 1. (a) Make a sketch of the region R bounded by y = sin(x), y = sin(x), x = 0, x = π. (b) Find the volume of the solid generated when R is rotated about the x-axis. P.T.O.
4 2 Calculus II, Quiz 2, September 2, Consider the region R given by the triangle with vertices (0, 0), (0, 2), (1, 2). (a) Make a sketch of the region R and of the solid S obtained by rotating R about the y-axis. (b) Find the volume of S. Which method are you using?
5 Department of Mathematical Sciences Instructor: Markus Schmidmeier Calculus II September 9, 2016 Name: Quiz 3 1. (a) Make a sketch of the region R in the first quadrant bounded by y = x 2, y = 1, x = 0. (b) Find the volume of the solid generated when R is revolved about the line y = 2. Which method are you using? (c) Find the volume of the solid generated when R is revolved about the line x = 1. Which method are you using? P.T.O.
6 6 Calculus II, Quiz 3, September 9, Make a sketch of the graph of the function given by y = x 3/2 on [0, 1] and find the arc length on the given interval.
7 Department of Mathematical Sciences Instructor: Markus Schmidmeier Calculus II September 16, 2016 Name: Quiz 4 1. (a) Find the area of the surface generated when the upper part of the circle x 2 + y 2 = 400 on the interval [0, 10] is rotated about the x-axis. (b) A 1.5 mm layer of paint is applied to one side of the surface in 1.(a). Find the approximate volume of paint needed. Assume that x and y are measured in meters. P.T.O.
8 6 Calculus II, Quiz 4, September 16, Suppose a force of 60N is required to stretch and hold a spring 0.5m from its equilibrium position. (a) Assuming the spring obeys Hooke s law, find the spring constant k. (b) How much work is required to compress the spring 0.25 m from its equilibrium position? (c) How much additional work is required to stretch the spring to 0.5 m if it has already been stretched to 0.25 m from its equilibrium position?
9 Department of Mathematical Sciences Instructor: Markus Schmidmeier Calculus II September 23, 2016 Name: 1. Find the following integrals: (a) 2 0 x x + 1 dx Quiz 5 (b) x 3 log(x) dx (c) sin(x) 5 dx P.T.O.
10 2 Calculus II, Quiz 5, September 23, Make a sketch of the region bounded by the graph of the function y = e x, the line x = log(5), the x-axis and the y-axis. Find the volume of the solid that is generated by revolving the region about the y-axis. Which method are you using?
11 Department of Mathematical Sciences Instructor: Markus Schmidmeier Calculus II September 30, 2016 Name: 1. Find the following integrals: (a) cos(x) 6 sin(x) 3 dx Quiz 6 (b) x + 1 x 2 4 dx (c) x + 1 x dx P.T.O.
12 2 Calculus II, Quiz 6, September 30, Make a sketch of the region bounded by the graph of the function y = 1 x + 1, the x-axis, the y-axis and the line x = 3. Find the volume of the solid that is generated by revolving the region about the y-axis. Which method are you using?
13 Department of Mathematical Sciences Instructor: Markus Schmidmeier Calculus II October 14, 2016 Name: 1. Find the following integrals: (a) 0 e 2x dx Quiz 7 (b) 0 1 x dx (c) 0 x x dx 6 best quizzes: average: letter grade: P.T.O.
14 2 Calculus II, Quiz 7, October 14, Make a sketch of the region bounded by the graph of the function 1 y = (x 1), 2 and the x-axis on the interval [2, ). Find the volume of the solid that is generated by revolving the region about the x-axis.
15 Department of Mathematical Sciences Instructor: Markus Schmidmeier Calculus II October 21, 2016 Name: Quiz 8 1. Several terms of a sequence {a n } n=1 are given. Find the next two terms of the sequence and state an explicit formula for the n-th term of the sequence. (a) {1, 4, 7, 10,...} (b) { 2, 4, 6, 8,...} (c) {27, 9, 3, 1,...} P.T.O.
16 2 Calculus II, Quiz 8, October 21, Find the limit for each of the following sequences or state that the limit does not exist. (a) {arctan(n)} (b) { } 7n n n n n 2 13n 5 (c) {( ) n } n + 4 n
SCORE. Exam 3. MA 114 Exam 3 Fall 2016
Exam 3 Name: Section and/or TA: Do not remove this answer page you will return the whole exam. You will be allowed two hours to complete this test. No books or notes may be used. You may use a graphing
Exam 3 Solutions. Multiple Choice Questions
MA 4 Exam 3 Solutions Fall 26 Exam 3 Solutions Multiple Choice Questions. The average value of the function f (x) = x + sin(x) on the interval [, 2π] is: A. 2π 2 2π B. π 2π 2 + 2π 4π 2 2π 4π 2 + 2π 2.
SCORE. Exam 3. MA 114 Exam 3 Fall 2016
Exam 3 Name: Section and/or TA: Do not remove this answer page you will return the whole exam. You will be allowed two hours to complete this test. No books or notes may be used. You may use a graphing
Level 1 Calculus Final Exam Day 1 50 minutes
Level 1 Calculus Final Exam 2013 Day 1 50 minutes Name: Block: Circle Teacher Name LeBlanc Normile Instructions Write answers in the space provided and show all work. Calculators okay but observe instructions
MA 126 CALCULUS II Wednesday, December 10, 2014 FINAL EXAM. Closed book - Calculators and One Index Card are allowed! PART I
CALCULUS II, FINAL EXAM 1 MA 126 CALCULUS II Wednesday, December 10, 2014 Name (Print last name first):................................................ Student Signature:.........................................................
SANDERSON HIGH SCHOOL AP CALCULUS AB/BC SUMMER REVIEW PACKET
SANDERSON HIGH SCHOOL AP CALCULUS AB/BC SUMMER REVIEW PACKET 017-018 Name: 1. This packet is to be handed in on Monday August 8, 017.. All work must be shown on separate paper attached to the packet. 3.
Spring 2017 Midterm 1 04/26/2017
Math 2B Spring 2017 Midterm 1 04/26/2017 Time Limit: 50 Minutes Name (Print): Student ID This exam contains 10 pages (including this cover page) and 5 problems. Check to see if any pages are missing. Enter
MA CALCULUS II Friday, December 09, 2011 FINAL EXAM. Closed Book - No calculators! PART I Each question is worth 4 points.
CALCULUS II, FINAL EXAM 1 MA 126 - CALCULUS II Friday, December 09, 2011 Name (Print last name first):...................................................... Signature:........................................................................
AP Calculus (BC) Chapter 10 Test No Calculator Section. Name: Date: Period:
AP Calculus (BC) Chapter 10 Test No Calculator Section Name: Date: Period: Part I. Multiple-Choice Questions (5 points each; please circle the correct answer.) 1. The graph in the xy-plane represented
AP Calculus AB. Review for Test: Applications of Integration
Name Review for Test: Applications of Integration AP Calculus AB Test Topics: Mean Value Theorem for Integrals (section 4.4) Average Value of a Function (manipulation of MVT for Integrals) (section 4.4)
PLEASE MARK YOUR ANSWERS WITH AN X, not a circle! 1. (a) (b) (c) (d) (e) 2. (a) (b) (c) (d) (e) (a) (b) (c) (d) (e) 4. (a) (b) (c) (d) (e)...
Math, Exam III November 6, 7 The Honor Code is in effect for this examination. All work is to be your own. No calculators. The exam lasts for hour and min. Be sure that your name is on every page in case
Spring 2015 Sample Final Exam
Math 1151 Spring 2015 Sample Final Exam Final Exam on 4/30/14 Name (Print): Time Limit on Final: 105 Minutes Go on carmen.osu.edu to see where your final exam will be. NOTE: This exam is much longer than
y = x 3 and y = 2x 2 x. 2x 2 x = x 3 x 3 2x 2 + x = 0 x(x 2 2x + 1) = 0 x(x 1) 2 = 0 x = 0 and x = (x 3 (2x 2 x)) dx
Millersville University Name Answer Key Mathematics Department MATH 2, Calculus II, Final Examination May 4, 2, 8:AM-:AM Please answer the following questions. Your answers will be evaluated on their correctness,
Integration. Tuesday, December 3, 13
4 Integration 4.3 Riemann Sums and Definite Integrals Objectives n Understand the definition of a Riemann sum. n Evaluate a definite integral using properties of definite integrals. 3 Riemann Sums 4 Riemann
Pre-Calculus Exam 2009 University of Houston Math Contest. Name: School: There is no penalty for guessing.
Pre-Calculus Exam 009 University of Houston Math Contest Name: School: Please read the questions carefully and give a clear indication of your answer on each question. There is no penalty for guessing.
MATH 1242 FINAL EXAM Spring,
MATH 242 FINAL EXAM Spring, 200 Part I (MULTIPLE CHOICE, NO CALCULATORS).. Find 2 4x3 dx. (a) 28 (b) 5 (c) 0 (d) 36 (e) 7 2. Find 2 cos t dt. (a) 2 sin t + C (b) 2 sin t + C (c) 2 cos t + C (d) 2 cos t
1. Use the properties of exponents to simplify the following expression, writing your answer with only positive exponents.
Math120 - Precalculus. Final Review. Fall, 2011 Prepared by Dr. P. Babaali 1 Algebra 1. Use the properties of exponents to simplify the following expression, writing your answer with only positive exponents.
Chapter 6 Some Applications of the Integral
Chapter 6 Some Applications of the Integral Section 6.1 More on Area a. Representative Rectangle b. Vertical Separation c. Example d. Integration with Respect to y e. Example Section 6.2 Volume by Parallel
(a) Write down the value of q and of r. (2) Write down the equation of the axis of symmetry. (1) (c) Find the value of p. (3) (Total 6 marks)
1. Let f(x) = p(x q)(x r). Part of the graph of f is shown below. The graph passes through the points ( 2, 0), (0, 4) and (4, 0). (a) Write down the value of q and of r. (b) Write down the equation of
NO CALCULATORS: 1. Find A) 1 B) 0 C) D) 2. Find the points of discontinuity of the function y of discontinuity.
AP CALCULUS BC NO CALCULATORS: MIDTERM REVIEW 1. Find lim 7x 6x x 7 x 9. 1 B) 0 C) D). Find the points of discontinuity of the function y of discontinuity. x 9x 0. For each discontinuity identify the type
Practice Exam # (.95.5) (696850) Due: Tue May 1 015 10:0 AM PDT Question 1 3 5 6 7 8 9 10 11 1 13 1 15 16 17 1. Question Details SCalcET7.9.06. [1835869] A particle is moving with the given data. Find
Math 152 Take Home Test 1
Math 5 Take Home Test Due Monday 5 th October (5 points) The following test will be done at home in order to ensure that it is a fair and representative reflection of your own ability in mathematics I
Practice Exam I. Summer Term I Kostadinov. MA124 Calculus II Boston University
student: Practice Exam I Problem 1: Find the derivative of the functions T 1 (x), T 2 (x), T 3 (x). State the reason of your answers. a) T 1 (x) = x 2t dt 2 b) T 2 (x) = e x ln(t2 )dt c) T 3 (x) = x 2
There are some trigonometric identities given on the last page.
MA 114 Calculus II Fall 2015 Exam 4 December 15, 2015 Name: Section: Last 4 digits of student ID #: No books or notes may be used. Turn off all your electronic devices and do not wear ear-plugs during
Section 8.7. Taylor and MacLaurin Series. (1) Definitions, (2) Common Maclaurin Series, (3) Taylor Polynomials, (4) Applications.
Section 8.7 Taylor and MacLaurin Series (1) Definitions, (2) Common Maclaurin Series, (3) Taylor Polynomials, (4) Applications. MATH 126 (Section 8.7) Taylor and MacLaurin Series The University of Kansas
AP Calculus Exam Format and Calculator Tips:
AP Calculus Exam Format and Calculator Tips: Exam Format: The exam is 3 hours and 15 minutes long and has two sections multiple choice and free response. A graphing calculator is required for parts of
Calculus I. 1. Limits and Continuity
2301107 Calculus I 1. Limits and Continuity Outline 1.1. Limits 1.1.1 Motivation:Tangent 1.1.2 Limit of a function 1.1.3 Limit laws 1.1.4 Mathematical definition of a it 1.1.5 Infinite it 1.1. Continuity
Resources: http://www.calcchat.com/book/calculus-9e/ http://apcentral.collegeboard.com/apc/public/courses/teachers_corner/27.html http://www.calculus.org/ http://cow.math.temple.edu/ http://www.mathsisfun.com/calculus/
Math 12 Final Exam Review 1
Math 12 Final Exam Review 1 Part One Calculators are NOT PERMITTED for this part of the exam. 1. a) The sine of angle θ is 1 What are the 2 possible values of θ in the domain 0 θ 2π? 2 b) Draw these angles
Higher Mathematics Course Notes
Higher Mathematics Course Notes Equation of a Line (i) Collinearity: (ii) Gradient: If points are collinear then they lie on the same straight line. i.e. to show that A, B and C are collinear, show that
Problem. Set up the definite integral that gives the area of the region. y 1 = x 2 6x, y 2 = 0. dx = ( 2x 2 + 6x) dx.
Wednesday, September 3, 5 Page Problem Problem. Set up the definite integral that gives the area of the region y x 6x, y Solution. The graphs intersect at x and x 6 and y is the uppermost function. So
UNIVERSITY OF REGINA Department of Mathematics and Statistics. Calculus I Mathematics 110. Final Exam, Winter 2013 (April 25 th )
UNIVERSITY OF REGINA Department of Mathematics and Statistics Calculus I Mathematics 110 Final Exam, Winter 2013 (April 25 th ) Time: 3 hours Pages: 11 Full Name: Student Number: Instructor: (check one)
Polynomial Degree Leading Coefficient. Sign of Leading Coefficient
Chapter 1 PRE-TEST REVIEW Polynomial Functions MHF4U Jensen Section 1: 1.1 Power Functions 1) State the degree and the leading coefficient of each polynomial Polynomial Degree Leading Coefficient y = 2x
AP Calculus Free-Response Questions 1969-present AB
AP Calculus Free-Response Questions 1969-present AB 1969 1. Consider the following functions defined for all x: f 1 (x) = x, f (x) = xcos x, f 3 (x) = 3e x, f 4 (x) = x - x. Answer the following questions
MATH 151, FALL 2017 COMMON EXAM 2, VERSION B. LAST NAME (print) : FIRST NAME (print): INSTRUCTOR : SECTION NUMBER: DIRECTIONS THE AGGIE HONOR CODE
MATH 5, FALL 7 COMMON EXAM, VERSION B LAST NAME (print) : FIRST NAME (print): INSTRUCTOR : SECTION NUMBER: DIRECTIONS. The use of a calculator, laptop, or computer is prohibited.. TURN OFF cell phones
M152: Calculus II Midterm Exam Review
M52: Calculus II Midterm Exam Review Chapter 4. 4.2 : Mean Value Theorem. - Know the statement and idea of Mean Value Theorem. - Know how to find values of c making the theorem true. - Realize the importance
Mathematics 111 (Calculus II) Laboratory Manual
Mathematics (Calculus II) Laboratory Manual Department of Mathematics & Statistics University of Regina nd edition prepared by Patrick Maidorn, Fotini Labropulu, and Robert Petry University of Regina Department
A.P. Calculus BC Test Four Section Two Free-Response Calculators Allowed Time 45 minutes Number of Questions 3
A.P. Calculus BC Test Four Section Two Free-Response Calculators Allowed Time 45 minutes Number of Questions Each of the three questions is worth 9 points. The maximum possible points earned on this section
Free Response Questions Compiled by Kaye Autrey for face-to-face student instruction in the AP Calculus classroom
Free Response Questions 1969-010 Compiled by Kaye Autrey for face-to-face student instruction in the AP Calculus classroom 1 AP Calculus Free-Response Questions 1969 AB 1 Consider the following functions
MATH 152, SPRING 2017 COMMON EXAM I - VERSION A
MATH 152, SPRING 2017 COMMON EXAM I - VERSION A LAST NAME(print): FIRST NAME(print): INSTRUCTOR: SECTION NUMBER: DIRECTIONS: 1. The use of a calculator, laptop or computer is prohibited. 2. TURN OFF cell
Midterm 1 practice UCLA: Math 32B, Winter 2017
Midterm 1 practice UCLA: Math 32B, Winter 2017 Instructor: Noah White Date: Version: practice This exam has 4 questions, for a total of 40 points. Please print your working and answers neatly. Write your
By providing my signature below I acknowledge that this is my work, and I did not get any help from anyone else:
University of Georgia Department of Mathematics Math 2250 Final Exam Spring 2016 By providing my signature below I acknowledge that this is my work, and I did not get any help from anyone else: Name (sign):
Math 1: Calculus with Algebra Midterm 2 Thursday, October 29. Circle your section number: 1 Freund 2 DeFord
Math 1: Calculus with Algebra Midterm 2 Thursday, October 29 Name: Circle your section number: 1 Freund 2 DeFord Please read the following instructions before starting the exam: This exam is closed book,
1. Use the properties of exponents to simplify the following expression, writing your answer with only positive exponents.
Math120 - Precalculus. Final Review Prepared by Dr. P. Babaali 1 Algebra 1. Use the properties of exponents to simplify the following expression, writing your answer with only positive exponents. (a) 5
MATH 1271 Wednesday, 5 December 2018
MATH 27 Wednesday, 5 December 208 Today: Review for Exam 3 Exam 3: Thursday, December 6; Sections 4.8-6. /6 Information on Exam 3 Six numbered problems First problem is multiple choice (five parts) See
The Princeton Review AP Calculus BC Practice Test 2
0 The Princeton Review AP Calculus BC Practice Test CALCULUS BC SECTION I, Part A Time 55 Minutes Number of questions 8 A CALCULATOR MAY NOT BE USED ON THIS PART OF THE EXAMINATION Directions: Solve each
MATH 115 Precalculus Spring, 2015, V1.2
MULTIPLE CHOICE 1. Solve, and express the answer in interval notation: 6 5x 4. 1. A. (, 2] [2/5, ) B. [2/5, 2] C. (, 2/5] D. (, 2/5] [2, ) 2. Which of the following polynomials has a graph which exhibits
Summer Assignment Directions:
Name: Block: Date: AP Calculus AB Summer Assignment Mr. Carter Welcome to AP Calculus AB! This fall will begin an exciting, challenging journey through the world of mathematics. You will challenge yourself
a. Determine the potential energy of the spring as a function of displacement.
PSI AP Physics C Work and Energy (With Calculus) Free Response Problems Use g = 10 m/s 2 1. A spring is found with a force that doesn t obey Hooke s Law: F = -kx 2. This spring is placed on a horizontal
Spring /06/2009
MA 123 Elementary Calculus FINAL EXAM Spring 2009 05/06/2009 Name: Sec.: Do not remove this answer page you will return the whole exam. You will be allowed two hours to complete this test. No books or
Grade 11 or 12 Pre-Calculus
Grade 11 or 12 Pre-Calculus Strands 1. Polynomial, Rational, and Radical Relationships 2. Trigonometric Functions 3. Modeling with Functions Strand 1: Polynomial, Rational, and Radical Relationships Standard
2. Which of the following is an equation of the line tangent to the graph of f(x) = x 4 + 2x 2 at the point where
AP Review Chapter Name: Date: Per: 1. The radius of a circle is decreasing at a constant rate of 0.1 centimeter per second. In terms of the circumference C, what is the rate of change of the area of the
Mathematics Extension 1
NSW Education Standards Authority 08 HIGHER SCHOOL CERTIFICATE EXAMINATION Mathematics Extension General Instructions Reading time 5 minutes Working time hours Write using black pen Calculators approved
MTH 122: Section 204. Plane Trigonometry. Test 1
MTH 122: Section 204. Plane Trigonometry. Test 1 Section A: No use of calculator is allowed. Show your work and clearly identify your answer. 1. a). Complete the following table. α 0 π/6 π/4 π/3 π/2 π
Determining Average and Instantaneous Rates of Change
MHF 4UI Unit 9 Day 1 Determining Average and Instantaneous Rates of Change From Data: During the 1997 World Championships in Athens, Greece, Maurice Greene and Donovan Bailey ran a 100 m race. The graph
GUIDED NOTES 6.4 GRAPHS OF LOGARITHMIC FUNCTIONS
GUIDED NOTES 6.4 GRAPHS OF LOGARITHMIC FUNCTIONS LEARNING OBJECTIVES In this section, you will: Identify the domain of a logarithmic function. Graph logarithmic functions. FINDING THE DOMAIN OF A LOGARITHMIC
8.2 APPLICATIONS TO GEOMETRY
8.2 APPLICATIONS TO GEOMETRY In Section 8.1, we calculated volumes using slicing and definite integrals. In this section, we use the same method to calculate the volumes of more complicated regions as
MATH 251 Examination I October 9, 2014 FORM A. Name: Student Number: Section:
MATH 251 Examination I October 9, 2014 FORM A Name: Student Number: Section: This exam has 14 questions for a total of 100 points. Show all you your work! In order to obtain full credit for partial credit
DO NOT WRITE ABOVE THIS LINE!! MATH 181 Final Exam. December 8, 2016
MATH 181 Final Exam December 8, 2016 Directions. Fill in each of the lines below. Circle your instructor s name and write your TA s name. Then read the directions that follow before beginning the exam.
5, tan = 4. csc = Simplify: 3. Simplify: 4. Factor and simplify: cos x sin x cos x
Precalculus Final Review 1. Given the following values, evaluate (if possible) the other four trigonometric functions using the fundamental trigonometric identities or triangles csc = - 3 5, tan = 4 3.
In general, if we start with a function f and want to reverse the differentiation process, then we are finding an antiderivative of f.
Math 1410 Worksheet #27: Section 4.9 Name: Our final application of derivatives is a prelude to what will come in later chapters. In many situations, it will be necessary to find a way to reverse the differentiation
Final Exam SOLUTIONS MAT 131 Fall 2011
1. Compute the following its. (a) Final Exam SOLUTIONS MAT 131 Fall 11 x + 1 x 1 x 1 The numerator is always positive, whereas the denominator is negative for numbers slightly smaller than 1. Also, as
Chapter 2 Differentiation. 2.1 Tangent Lines and Their Slopes. Calculus: A Complete Course, 8e Chapter 2: Differentiation
Chapter 2 Differentiation 2.1 Tangent Lines and Their Slopes 1) Find the slope of the tangent line to the curve y = 4x x 2 at the point (-1, 0). A) -1 2 C) 6 D) 2 1 E) -2 2) Find the equation of the tangent
C3 Revision Questions. (using questions from January 2006, January 2007, January 2008 and January 2009)
C3 Revision Questions (using questions from January 2006, January 2007, January 2008 and January 2009) 1 2 1. f(x) = 1 3 x 2 + 3, x 2. 2 ( x 2) (a) 2 x x 1 Show that f(x) =, x 2. 2 ( x 2) (4) (b) Show
MATH 151 Engineering Mathematics I
MATH 151 Engineering Mathematics I Fall 2017, WEEK 14 JoungDong Kim Week 14 Section 5.4, 5.5, 6.1, Indefinite Integrals and the Net Change Theorem, The Substitution Rule, Areas Between Curves. Section
Review: Exam Material to be covered: 6.1, 6.2, 6.3, 6.5 plus review of u, du substitution.
Review: Exam. Goals for this portion of the course: Be able to compute the area between curves, the volume of solids of revolution, and understand the mean value of a function. We had three basic volumes:
Summer Math Packet for AP Calculus BC
Class: Date: Summer Math Packet for AP Calculus BC 018-19 1. Find the smallest value in the range of the function f (x) = x + 4x + 40. a. 4 b. 5 c. 6 d. 7 e. 8 f. 16 g. 4 h. 40. Find the smallest value
Math 116 Second Midterm March 20, 2013
Math 6 Second Mierm March, 3 Name: EXAM SOLUTIONS Instructor: Section:. Do not open this exam until you are told to do so.. This exam has 3 pages including this cover. There are 8 problems. Note that the
MATH 1271 Monday, 21 November 2018
MATH 1271 Monday, 21 November 218 Today: Section 5.4 - Indefinite Integrals and the Theorem Homework: 5-17 odd, 21-45 odd, 51-63 odd, 67, 71 1/13 Def Total displacement is the integral of the velocity
Learning Objectives for Math 166
Learning Objectives for Math 166 Chapter 6 Applications of Definite Integrals Section 6.1: Volumes Using Cross-Sections Draw and label both 2-dimensional perspectives and 3-dimensional sketches of the
d` = 1+( dy , which is part of the cone.
7.5 Surface area When we did areas, the basic slices were rectangles, with A = h x or h y. When we did volumes of revolution, the basic slices came from revolving rectangles around an axis. Depending on
LHS Algebra Pre-Test
Your Name Teacher Block Grade (please circle): 9 10 11 12 Course level (please circle): Honors Level 1 Instructions LHS Algebra Pre-Test The purpose of this test is to see whether you know Algebra 1 well
Force versus distance graph
Force versus distance graph Objectives Investigate examples of kinetic and potential energy and their transformations. Calculate work from the area under the force vs. distance graph. Relate the net work
Math 221 Exam III (50 minutes) Friday April 19, 2002 Answers
Math Exam III (5 minutes) Friday April 9, Answers I. ( points.) Fill in the boxes as to complete the following statement: A definite integral can be approximated by a Riemann sum. More precisely, if a
Summer Term I Kostadinov. MA124 Calculus II Boston University. Evaluate the definite integrals. sin(ln(x)) x
student: Exam I Problem : Evaluate the indefinite integrals 2e x + cos(x) dx 8x 3 + 5 4 x dx Problem 2: Evaluate the definite integrals 4 3 x + x dx π/2 π/6 sin(x) dx Problem 3: Evaluate the definite integrals
University of Toronto MAT137Y1 Calculus! Test 2 1 December 2017 Time: 110 minutes
University of Toronto MAT137Y1 Calculus! Test 2 1 December 2017 Time: 110 minutes Please complete this cover page with ALL CAPITAL LETTERS. Last name......................................................................................
Hour Exam #1 Math 3 Oct. 20, 2010
Hour Exam #1 Math 3 Oct. 20, 2010 Name: On this, the first of the two Math 3 hour-long exams in Fall 2010, and on the second hour-exam, and on the final examination I will work individually, neither giving
WebAssign hw1.1 (Homework)
WebAssign hw1.1 (Homework) Current Score : / 71 Due : Wednesday, May 31 2017 07:25 AM PDT Michael Lee Math261(Calculus I), section 1049, Spring 2017 Instructor: Michael Lee 1. /1 pointsscalc8 1.1.002.
The dimensions of an object tend to change when forces are
L A B 8 STRETCHING A SPRING Hooke s Law The dimensions of an object tend to change when forces are applied to the object. For example, when opposite forces are applied to both ends of a spring, the spring
UNIT 3: DERIVATIVES STUDY GUIDE
Calculus I UNIT 3: Derivatives REVIEW Name: Date: UNIT 3: DERIVATIVES STUDY GUIDE Section 1: Section 2: Limit Definition (Derivative as the Slope of the Tangent Line) Calculating Rates of Change (Average
Pre-Calculus Spring Final Exam Review Guide
Pre-Calculus Spring Final Exam Review Guide The Final Exam will cover: Chapter 4, Chapter 5, Polar Graphing, Solving systems of equations with Matrices (part of section 7.3), Partial Fraction Decomposition
The Definite Integral as an Accumulator
The Definite Integral as an Accumulator Louis A. Talman Department of Mathematical & Computer Sciences Metropolitan State College of Denver May, 5 In the last few years, the committee that writes the AP
Math 190 (Calculus II) Final Review
Math 90 (Calculus II) Final Review. Sketch the region enclosed by the given curves and find the area of the region. a. y = 7 x, y = x + 4 b. y = cos ( πx ), y = x. Use the specified method to find the
c) xy 3 = cos(7x +5y), y 0 = y3 + 7 sin(7x +5y) 3xy sin(7x +5y) d) xe y = sin(xy), y 0 = ey + y cos(xy) x(e y cos(xy)) e) y = x ln(3x + 5), y 0
Some Math 35 review problems With answers 2/6/2005 The following problems are based heavily on problems written by Professor Stephen Greenfield for his Math 35 class in spring 2005. His willingness to
Distance and Velocity
Distance and Velocity - Unit #8 : Goals: The Integral Determine how to calculate the area described by a function. Define the definite integral. Explore the relationship between the definite integral and
Multiple Choice Answers. MA 114 Calculus II Spring 2013 Final Exam 1 May Question
MA 114 Calculus II Spring 2013 Final Exam 1 May 2013 Name: Section: Last 4 digits of student ID #: This exam has six multiple choice questions (six points each) and five free response questions with points
Practice Exam 1 Solutions
Practice Exam 1 Solutions 1a. Let S be the region bounded by y = x 3, y = 1, and x. Find the area of S. What is the volume of the solid obtained by rotating S about the line y = 1? Area A = Volume 1 1
Below is a list of topics covered in the packet with formulas and helpful websites:
Dear Student I Please find attached your summer review packet for Academic Calculus. The problems in this packet are taken from Precalculus and they should be familiar to you. However I if you need review
University of Georgia Department of Mathematics. Math 2250 Final Exam Fall 2016
University of Georgia Department of Mathematics Math 2250 Final Exam Fall 2016 By providing my signature below I acknowledge that I abide by the University s academic honesty policy. This is my work, and
MATH 151, SPRING 2018
MATH 151, SPRING 2018 COMMON EXAM II - VERSIONBKEY LAST NAME(print): FIRST NAME(print): INSTRUCTOR: SECTION NUMBER: DIRECTIONS: 1. The use of a calculator, laptop or computer is prohibited. 2. TURN OFF
Calculus with the Graphing Calculator
Calculus with the Graphing Calculator Using a graphing calculator on the AP Calculus exam Students are expected to know how to use their graphing calculators on the AP Calculus exams proficiently to accomplish
Math 106 Answers to Exam 3a Fall 2015
Math 6 Answers to Exam 3a Fall 5.. Consider the curve given parametrically by x(t) = cos(t), y(t) = (t 3 ) 3, for t from π to π. (a) (6 points) Find all the points (x, y) where the graph has either a vertical
4 The Trigonometric Functions
Mathematics Learning Centre, University of Sydney 8 The Trigonometric Functions The definitions in the previous section apply to between 0 and, since the angles in a right angle triangle can never be greater
What students need to know for CALCULUS (Regular, AB and BC) Students expecting to take Calculus should demonstrate the ability to:
What students need to know for CALCULUS (Regular, AB and BC) Students expecting to take Calculus should demonstrate the ability to: General: keep an organized notebook take good notes complete homework
5 Trigonometric Functions
5 Trigonometric Functions 5.1 The Unit Circle Definition 5.1 The unit circle is the circle of radius 1 centered at the origin in the xyplane: x + y = 1 Example: The point P Terminal Points (, 6 ) is on
Multiple Choice Answers. MA 113 Calculus I Spring 2018 Exam 2 Tuesday, 6 March Question
MA 113 Calculus I Spring 2018 Exam 2 Tuesday, 6 March 2018 Name: Section: Last 4 digits of student ID #: This exam has 12 multiple choice questions (five points each) and 4 free response questions (ten
Calculus is Cool. Math 160 Calculus for Physical Scientists I Exam 1 September 18, 2014, 5:00-6:50 pm. NAME: Instructor: Time your class meets:
NAME: Instructor: Time your class meets: Math 160 Calculus for Physical Scientists I Exam 1 September 18, 2014, 5:00-6:50 pm How can it be that mathematics, being after all a product of human thought independent
Solutionbank Edexcel AS and A Level Modular Mathematics
Page of Exercise A, Question The curve C, with equation y = x ln x, x > 0, has a stationary point P. Find, in terms of e, the coordinates of P. (7) y = x ln x, x > 0 Differentiate as a product: = x + x
Limits and Continuity. 2 lim. x x x 3. lim x. lim. sinq. 5. Find the horizontal asymptote (s) of. Summer Packet AP Calculus BC Page 4
Limits and Continuity t+ 1. lim t - t + 4. lim x x x x + - 9-18 x-. lim x 0 4-x- x 4. sinq lim - q q 5. Find the horizontal asymptote (s) of 7x-18 f ( x) = x+ 8 Summer Packet AP Calculus BC Page 4 6. x
Department of Mathematical 1 Limits. 1.1 Basic Factoring Example. x 1 x 2 1. lim
Contents 1 Limits 2 1.1 Basic Factoring Example...................................... 2 1.2 One-Sided Limit........................................... 3 1.3 Squeeze Theorem..........................................