Waterloo - MATH - 138

MATH 138Things to know for the nal examYour nal exam on April 9 will include the broad spectrum of material that we have covered. More weight is placed on material since the mid-term. However, much of the later material depends on solid knowledge of ear

Waterloo - MATH - 138

Final exam Grad TA schedule for Math 138 Winter 2010 Math Faculty Tutorial Center MC4066Time Wednesday April 7 Thursday April 8 Friday April 99:00 AMExamRobert Garbary Kewei Yu Alejandra Vicente Colmenares Omar Leon SanchezClinton Loo Veronika Sheles

Waterloo - MATH - 138

MATH 138 Calculus 2, Solutions to MAPLE Lab Assignment 2Problem 1: Use MAPLE to list the rst 5 Taylor polynomials T1 (x), T2 (x), , T5 (x) centered at 0 for the 2x+1 function f (x) = 4x2 . Solution: The MAPLE commands f:=(2*x+1)/sqrt(4-x^2): n:=5: for i

Waterloo - MATH - 138

MATH 138 Maple Lab Assignment 1Differential Equations in MapleO with DEtools : O ode1 d diff y x , x = x C y x ; ode1 := O dsolve O dsolve O dsolve ode1, y 0 = 1 ode1, y 0 =K 1 ode1, y 0 =K 2 ; y x = K K x C 2 ex 1 ; y x = K Kx 1 ; y x = K K x K ex 1 O

Waterloo - MATH - 138

MATH 138 Calculus 2, MAPLE Lab Assignment 2Due: Monday, March 29 by 11:00 am in the MATH 138 drop boxes outside MC 4066. We can have MAPLE list the rst 7 Taylor polynomials T1 (x), T2 (x), , T7 (x) centered at 0 for the function f (x) = sin x using the f

Waterloo - MATH - 138

MATH 138 Maple Lab Assignment 1Due: Friday, February 26, by 11:00 a.m. in the MATH 138 dropboxes outside of MC 4066. This question is designed to give you some familiarity with the use of Maple in solving differential equations. For practice, type the fo

Waterloo - MATH - 138

Exam Writing Tips1) Do NOT write an exam in order There seems to be a misconception among many students that the questions on an exam are ordered from easy to hard. In fact, many exams I have written as both a student and a teacher had the easy questions

Waterloo - MATH - 138

MATH 138 Assignment 10 SolutionsProblem 1: You may have wondered why odd functions are called odd, and even functions are called even. Here is a possible reason. Suppose f (x) = a0 + a1 x + a2 x2 + a3 x3 + a4 x4 + . . . for x in an interval (R, R). If f

Waterloo - MATH - 138

MATH 138Assignment 11NOT TO BE HANDED INOur course ends with an introduction to parametrized curves. This material is covered in Stewart, Sections 10.1 and 10.2. Section 10.1 is intended to get you familiar with the notion of a parametrized curve. The

Waterloo - MATH - 138

MATH 138Assignment 10Due by: 11 a.m., MONDAY, March 29Place your assignment in the correct drop box. If your assignment falls into the wrong box, there is a good chance it will become lost. Print your name and I.D. number at the top of the rst page of

Waterloo - MATH - 138

MATH 138 Calculus 2, Solutions to Assignment 9Problem 1: For each series below determine whether it converges absolutely, conditionally, or not at all.(a)(1)nn=1n10 2n n10 . Then 2n n+1 n10Solution: Let an =an+1 (n + 1)10 2n 10 = = an 2n+1 n Thus

Waterloo - MATH - 138

MATH 138 ASSIGNMENT 8 SOLUTIONS WINTER 20101 1. The Integral Test can be applied since f (x) = (2x+1)7 is continuous, positive and decreasing on [1, ). By the remainder estimate for the Integral Test, we want to nd n such that n 1 dx < 105 . (2x + 1)7t

Waterloo - MATH - 138

MATH 138Assignment 9Due by: 11 a.m., Friday, March 19Place your assignment in the correct drop box. If your assignment falls into the wrong box, there is a good chance it will become lost. Print your name and I.D. number at the top of the rst page of y

Waterloo - MATH - 138

MATH 138Assignment 8Due by: 11 a.m., Friday, March 12Place your assignment in the correct drop box. If your assignment falls into the wrong box, there is a good chance it will become lost. Print your name and I.D. number at the top of the rst page of y

Waterloo - MATH - 138

MATH 138Assignment 7Due by: 11 a.m., Friday, March 5Place your assignment in the correct drop box. If your assignment falls into the wrong box, there is a good chance it will become lost. Print your name and I.D. number at the top of the rst page of yo

Waterloo - MATH - 138

MATH 138 Assignment 7 SolutionsProblem 1: Find the sums of the following series. n (a) 23n1 n=0 Solution:n 23n1=n=0n=02 n = (23 )n 82n=0 8nNote: Geometric Series with a = 2, |r| < 1=2 1=16 83 + 2n 3n+2 n=0 Solution: (b)n=0 3 + 2n = 3n+2

Waterloo - MATH - 138

MATH 138 Calculus 2, Solutions to Assignment 6Problem 1: We can sense that 3 + 3+12 n12 n 9 as n . Given any12 n> 0, show that if n >1 n27, then 9 < . This proves from scratch that 3 +1 n2 9. Hint. You know that12 n 6 n1 nalways.Solution:

Waterloo - MATH - 138

MATH 138 Assignment 5 Solutions Winter 2010Note: A rst-order linear dierential equation (D.E.) is of the form dy + P (x) y = Q (x) dx and the integrating factor for such a D.E. is R I (x) = e P (x)dx . dy + y = cos (ex ) dx is of the form (1) with P (x)

Waterloo - MATH - 138

MATH 138Assignment 6Due by: 11 a.m., Friday, February 26Place your assignment in the correct drop box. If your assignment falls into the wrong box, there is a good chance it will become lost. Print your name and I.D. number at the top of the rst page o

Waterloo - MATH - 138

MATH 138Assignment 5Due by: 11 a.m., Friday, February 12Place your assignment in the correct drop box. If your assignment falls into the wrong box, there is a very good chance it will become lost. Print your name and I.D. number at the top of the rst p

Waterloo - MATH - 138

MATH 138Assignment 4Due by: 11 a.m., Friday, February 5Place your assignment in the correct drop box. If your assignment falls into the wrong box, there is a very good chance it will become lost. Print your name and I.D. number at the top of the rst pa

Waterloo - MATH - 138

Waterloo - MATH - 138

MATH 138Assignment 3Due by: 11 a.m., Friday, January 29.Place your assignment in the correct drop box. If your assignment falls into the wrong box, there is a very good chance it will get lost. Print your name and I.D. number at the top of the rst page

Waterloo - MATH - 138

MATH 138Assignment 1Due by: 11 a.m., Friday, January 15.Place your assignment in the correct drop box. If your assignment falls into the wrong box, there is a very good chance it will get lost. Print your name and I.D. number at the top of the rst page

Waterloo - MATH - 138

MATH 138Assignment 2Due by: 11 a.m., Friday, January 22.Place your assignment in the correct drop box. If your assignment falls into the wrong box, there is a very good chance it will get lost. Print your name and I.D. number at the top of the rst page

Memorial University - BUSI - 5301

Chapter 6 Definitions: Economies of Scale: Achieving lower costs through large volume production often made possible by global expansion. Economies of Scope: Achieving economies by having a presence in many product lines, technologies or geographic areas.

University of the West Indies at Mona - ECON - 1003

University of the West Indies at Mona - ECON - 1003

University of the West Indies at Mona - ECON - 1003

University of the West Indies at Mona - ECON - 1003

University of the West Indies at Mona - ECON - 1003

University of the West Indies at Mona - ECON - 1003

University of the West Indies at Mona - ECON - 1003

University of the West Indies at Mona - ECON - 1003

University of the West Indies at Mona - ECON - 1003

University of the West Indies at Mona - ECON - 1003

University of the West Indies at Mona - ECON - 1003

University of the West Indies at Mona - ECON - 1003

University of the West Indies at Mona - ECON - 1003

University of the West Indies at Mona - ECON - 1003

University of the West Indies at Mona - ECON - 1003

University of the West Indies at Mona - ECON - 1003

University of the West Indies at Mona - ECON - 1003

ECON1003Mathematics for the Social SciencesTopic 6: Sequences and Series Lecturer: Marlon Tracey1ObjectiveoAt the end of this topic, students should be able to:oDistinguish between a sequence and a series Distinguish between arithmetic and geometr

University of the West Indies at Mona - ECON - 1003

EC14C Problem Paper # 3 Exponential and Logarithmic Functions1. The demand equation for a certain product is given by p = 500 0.5e 0.004 x . Find the price p for a demand of (a) x = 1000 units and (b) x = 1500 units. 2. The population of a town increases

University of the West Indies at Mona - ECON - 1003

Find the matrix solution to the systems in exercises 4-6 using Cramers rule.

University of the West Indies at Mona - ECON - 1003

ECON1003Mathematics for the Social SciencesTopic 5: Matrix Algebra Lecturer: Marlon Tracey1ObjectiveoAt the end of this topic, students should be able to:oDo operations on matrices. Determine the determinant and inverse of a matrix. Identify the p

University of the West Indies at Mona - ECON - 1003

ECON1003Mathematics for the Social SciencesTopic 7: Limits and Continuity Lecturer: Marlon Tracey1ObjectiveoAt the end of this topic, students should be able to:oDefine the limit of a function. Compute the limits of polynomial and rational functio

University of the West Indies at Mona - ECON - 1003

ECON1003Mathematics for the Social SciencesTopic 1: Functions Lecturer: Marlon TraceyObjectiveoAt the end of this topic, students should be able to:o o o o o oDefine and identify a function Distinguish among types of functions Derive composite and

University of the West Indies at Mona - ECON - 1003

THE UNIVERSITY OF THE WEST INDIES EXAMINATION OF April/May, 2005Code and Name of Course: EC14C: Mathematics for the Social Sciences Date and Time: Paper: BSc Duration: 2 HoursINSTRUCTIONS TO CANDIDATES: This paper has7pages and24questionsThe paper

University of the West Indies at Mona - ECON - 1003

THE UNIVERSITY OF THE WEST INDIES EXAMINATION of May, 2007Code and Name of Course: EC14C Mathematics for the Social Sciences Date and Time: Paper: BSc Duration: 2 HoursINSTRUCTIONS TO CANDIDATES: This paper has 3 page(s) and 4 questionsThis paper has O

University of the West Indies at Mona - ECON - 1003

THE UNIVERSITY OF THE WEST INDIES EXAMINATION of December 2007Code and Name of Course: EC14C Mathematics for the Social Sciences Date and Time:Paper: BSc Duration: 2 HoursINSTRUCTIONS TO CANDIDATES: This paper has 5 page(s) and 4 questions Answer any

University of the West Indies at Mona - ECON - 1003

THE UNIVERSITY OF THE WEST INDIES EXAMINATION of December, 2006Code and Name of Course: EC14C Mathematics for the Social Sciences Date and Time: Paper: BSc Duration: 2 HoursINSTRUCTIONS TO CANDIDATES: This paper has 5 page(s) and 5 questionsThis paper

University of the West Indies at Mona - ECON - 1003

THE UNIVERSITY OF THE WEST INDIES EXAMINATION OF DECEMBER, 2005Code and Name of Course: EC14C: Mathematics for the Social Sciences Date and Time: Paper: BSc Duration: 2 HoursINSTRUCTIONS TO CANDIDATES: This paper has6pages and24questionsThe paper h

University of the West Indies at Mona - ECON - 1003

ECON1003/EC14CMathematics for the Social SciencesTopic 4: Exponential and Logarithmic Functions Lecturer: Marlon Tracey1ObjectiveoAt the end of this topic, students should be able to:oDescribe the graph of an exponential function. Describe the nat

University of the West Indies at Mona - ECON - 1003

THE UNIVERSITY OF THE WEST INDIES EXAMINATION OF December, 2004Code and Name of Course: EC14C: Mathematics for the Social Sciences Date and Time: Paper: BSc Duration: 2 HoursINSTRUCTIONS TO CANDIDATES: This paper has7pages and24questionsThe paper h

University of the West Indies at Mona - ECON - 1003

EC14C Problem Paper # 5 Sequences and SeriesSequences In Exercises 1-4, write the first five terms of the given sequence. 2n n 1. a n 2. a n (1) n 1 3n 1 n 12 3. a n 3n 14. a n (1) n enIn Exercises 5-6, write the first five terms of the given sequen

University of the West Indies at Mona - ECON - 1003

EC14C Problem Paper # 6 Limits and ContinuityIn Exercises 1-10, find the limits, if they exist. 1. lim ( x 3)x 22. lim 4x 123. limx 3x2 9 x34. limx 2 4x 4 x 2 x25. limx3 4x x 2 2 x 2 x 36. lim2( x h) 2 2 x 2 h 0 h4x 1 x x 2 1 lim6 x 1, x 1

University of the West Indies at Mona - ECON - 1003

EC14C Problem Paper #2 Inequalities and Complex NumbersInequalities In Exercises 1-5 find the solution sets to the linear inequalities and depict these on a number line. x 3 5x 1 1. 2 x 3 5x 4 2. 3. 6 x 7 14 34 63 4. 1 3x 4 7 5. 3 5 3x 6 2 In Exercises 6

University of the West Indies at Mona - ECON - 1003

EC 14C Problem Paper #1 FunctionsIn Exercises 1-4, evaluate the function at the specified value and simplify the results. 1.f ( x) (a) f (2)x x(b) f (-2) (c) f x 2(d) f(x 1)2.2 x 1, x 0 f ( x) 2 x 2, x 0 (a) f (-1) (b) f (0)(c) f (1)(d) f (2)3.

University of the West Indies at Mona - ECON - 1003

ECON1003Mathematics for the Social SciencesTopic 8: Differentiation Lecturer: Marlon Tracey1ObjectiveoAt the end of this topic, students should be able to:oDefine the concept of differentiation. Evaluate the differential of a function from first p

University of the West Indies at Mona - ECON - 1003

THE UNIVERSITY OF THE WEST INDIES EXAMINATION of JULY 2007Code and Name of Course: EC14C Mathematics for the Social Sciences Date and Time: Paper: BSc Duration: 2 HoursINSTRUCTIONS TO CANDIDATES: This paper has 6 page(s) and FIVE (5) questions Answer