McMaster University Math 1A03/1ZA3 Fall 2013
Midterm 2 PRACTICE
Duration: 90 minutes
Instructors: M. Bays, D. Haskell, E. Harper, C.McLean
Name:
Student ID Number:
This test paper is printed on both sides of the page. There are 20 question on 6 pages. You
18
CONS
1999/11/6
page 18
P ROOF T HEORY
This sum is not infinite, because each formula has a finite length (strings as we
have defined them have finite lengths), so for some m, nm , nm+1 , nm+2 , . . . are
!l
all zero. Similarly, i=1 bi is shorthand for
Chapter Seven - Differential Equations
Chapter Seven - Differential Equations
7.1 Basic Definitions
Differential Equation
A differential equation is any equation which contains derivatives, either ordinary
derivatives or partial derivatives. There is one
Chapter six - Additional Techniques of Integration
Chapter Six - Additional Techniques of Integration
9.1 Integration by Parts
The following result is useful for simplifying certain types of integrals
Integration by parts Formula (9.1)
Proof
By the produc
AP Calculus Course Outline
AP Calculus Course Outline - 2015 Summer School
(4:00 - 6:30 pm on Saturdays and Sundays, 5 hrs/week, totally 58 hours)
Chapter 1 Limits and Continuity
1.1 Definitions of Limits
1.2 Continuity
1.3 Limits Properties
1.4 Other Bas
Chapter Five - Applications of the Definite Integral
Chapter Five - Applications of the Definite Integral
Applications of the Definite Integral
The definite integral is useful for solving a large variety of applied problems. In this
chapter we shall discu
AP Calculus Assignment Five (3) Further Applications of Integration
AP Calculus Assignment Five (3) Further Applications of Integration
1. A particle moves along a line in such a way that its position at time t is given by
s t 3 6t 2 9t 3 . When does the
Olympiads: AP Chemistry
COURSE: AP CHEMISTRY
INSTRUCTOR: Ms. J. Chong
OBJECTIVES
The AP Chemistry course at Olympiads is designed to supplement and help students taking AP
Chemistry in school. AP Chemistry is the equivalent of a first-year university gene
Chapter Five (2) Polar Coordinates
Chapter Five (2) Polar Coordinates
Up to this point weve dealt exclusively with the Cartesian (or Rectangular, or x-y)
coordinate system. However, as we will see, this is not always the easiest coordinate
system to work
AP Calculus Assignment for Chapter Five (2) Polar Coordinate System
AP Calculus Assignment for Chapter Five (2) Polar Coordinates
1. Sketch the graph of the curve C having indicated parametric equations, and find a
rectangular equation of the graph.
(a) x
AP Calculus Assignment Nine Infinite Series
AP Calculus Assignment Nine Infinite Series
1. Find the first four terms and lim a n , if it exists.
n
(a) an n /(3n 2)
(b) an (7 4n 2 ) /(3 2n 2 )
(c) an 1 (0.1) n
(d) an [(2n 1)(3n 1)] /( n 3 1)
(e) an (ln n)
Chapter Four - Antiderivatives and the Definite Integral
Chapter Four - Antiderivatives and the Definite Integral
4.9
Antiderivatives
In chapter 3 certain problems were stated in the form give a function g, find the
derivative g, find the function g. an e
AP Calculus Assignment Six Additional Techniques of Integration
AP Calculus Assignment Six Additional Techniques of Integration
1. Evaluate the integrals.
(a)
(e)
(i)
xe dx
x ln xdx
x(2 x 3)
x
(b)
(f)
99
(j)
dx
x sec x tan xdx
(g) sin x ln cos xdx
(k)
Chapter Nine Infinite Series
Chapter Nine Infinite Series
9.1
Infinite Sequences
Lets start off this section with a discussion of just what a sequence is. A sequence is
nothing more than a list of numbers written in a specific order. The list may or may n
Chapter One Limits and Continuity
Chapter One - Limits and Continuity
1.1 Definitions of Limits
We write lim f ( x) L and say the limit of f(x), as x approaches a, equals L if we can
x a
make the value of f(x) arbitrarily close to L (as close to L as we l
AP Calculus Assignment Five Applications of the Definite Integral
AP Calculus Assignment Five (1) Applications of the Definite Integral
In Questions 1 - 11, evaluate the area of the region whose boundaries are given.
1. The curve of y = x2, y = 0, x = 1,
xiv
CONS
1999/11/6
page xiv
S UBSTRUCTURAL L OGICS
Friends, especially Fernando Gros and Leanne Cutts, and many at Dickson
Baptist Church in Canberra and Trinity Chapel Macquarie in Sydney, helped me
stay human. Finally, my thanks and affection belong to
CONS
1999/11/6
page iv
First published 2000
by Routledge
11 New Fetter Lane, London EC4P 4EE
Simultaneously published in the USA and Canada
by Routledge
29 West 35th Street, New York, NY 10001
Routledge is an imprint of the Taylor & Francis Group
c 2000
AP Chemistry Homework
Name: _
AP Chemistry: Class 21 Homework
1. Write the IUPAC name for each compound:
2. Name the following compounds.
3. Consider the compo
CHEMISTRY 1AA3 Winter 2016: Information Sheets
These sheets provide answers to most of your questions about the organization of the course.
We suggest that, after reading them carefully, you keep them with your notes for future reference. The
online versi