Chapter 8 Exponential functions
8.1
Graph the following functions: (a) f (x) = x2 ex (b) f (x) = ln(x2 + 3) (c) f (x) = ln(e2x )
8.2
Express the following in terms of base e: (a) y = 3x (b) y =
1 7x
2 +2
(c) y = 15x
Express the following in terms of base

Chapter 13 More Dierential Equations
13.1
Consider the dierential equation dy = a by dt where a, b are constants. (a) Show that the function a Cebt b satises the above dierential equation for any constant C . y (t) = C= we also satisfy the initial conditi

Chapter 13 More Dierential Equations
13.1
Consider the dierential equation dy = a by dt
where a, b are constants. (a) Show that the function a Cebt b satises the above dierential equation for any constant C . y (t) = C= we also satisfy the initial conditi

All owls are carnivorous birds of prey and live mainly on a diet of insects and small rodents such as
mice, rats, and hares. Some owls are also specifically adapted to hunt fish. They are very adept in
hunting in their respective environments. Since owls

Chapter 11 Inverse Trigonometric functions
In this chapter, we investigate inverse trigonometric functions1 . As in other examples, the inverse of a given function leads to exchange of the roles of the dependent and independent variables, as well as the t

Chapter 10 Trigonometric functions
In this chapter we will explore periodic and oscillatory phenomena. The trigonometric functions will be the basis for much of what we construct1 , and hence, we rst introduce these and familiarize ourselves with their pr

Chapter 9 Exponential Growth and Decay: Dierential Equations
9.1 Observations about the exponential function
y = f (x) = ex namely, that dy = ex = y dx so that this function satises the relationship dy = y. dx We call this a dierential equation because it

Chapter 8 Exponential functions
In this chapter, we leave behind the power functions and polynomials, and explore a new type of function, exponential growth. We nd that this function is closely related to (uncontrolled) growth of living replicating organi

Chapter 7 The Chain Rule, Related Rates, and Implicit Dierentiation
7.1 Function composition
u x f
Figure 7.1: Shown in the diagram above is an example of function composition: An independent variable, x, is used to evaluate a function, and the result, u

Chapter 6 Optimization
In this chapter, we collect a variety of problems in which the ideas developed in earlier material are put to use. In particular, we will use calculus to find local (and global) maxima, and minima so as to get the best (optimal) val

Chapter 5 What the Derivative tells us about a function
The derivative of a function contains a lot of important information about the behaviour of a function. In this chapter we will focus on how properties of the rst and second derivative can be used to

Chapter 4 The Derivative
In our investigation so far, we have dened the notion of an instantaneous rate of change, and called this the derivative. We have also identied this mathematical concept with the slope of a tangent line to the graph of a function.

Chapter 3 Average velocity, Average Rates of Change, and Secant Lines
In this chapter, we extend the idea of slope of a straight line to a related concept for a curve. We will rst encounter the idea of an average slope, (also denoted average rate of chang

Chapter 2 Review of Simple Functions
In this chapter we review a few basic concepts related to functions, and introduce the simplest family of functions that have interesting, nontrivial properties: the power functions. We explore geometric and graphical

Chapter 1 Review of Straight Lines
We start with a brief review of properties of straight lines, since these properties are fundamentally important to our understanding of more advanced concepts (tangents, slopes, derivatives). Skills described in this in

Chapter 12 Approximation methods
12.1 Introduction
In this chapter we explore a few techniques for nding approximate solutions to problems of great practical signicance. The techniques here described are linked by a number of common features; most notably

Chapter 13 More Dierential Equations
13.1 Introduction
In our discussion of exponential functions, we briey encountered the idea of a dierential equation. We saw that verbal descriptions of the rate of change of a process (for example, the growth of a pop

Lecture Notes in Computer Science:
Authors Instructions for the Preparation
of Camera-Ready Contributions
to LNCS/LNAI Proceedings
Alfred Hofmann1 , Antje Endemann1 , Anna Kramer1 , Andrea Washington1 ,
urk3
Angelika Bernauer-Budiman2 , and Anita B
1
3
Sp

Journal of Animal Science
Guidelines for Creating Tables Using Microsoft Word
The best way to prepare a table in a manuscript is using the Microsoft Word Table function. These
instructions are for the 2003 version of Microsoft Word. For the 2007 version,

Two-column Notes
Two Column
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Overview
Each and every movement in each and every sport contains a great deal of
physics. In some sports, such as swimming and cross-country, the winner of a
competition is determined by who can move the fastest average speed. Other
sports, such as baske

Higher Physics
Resources Guide
November 2014
Transforming lives through learning
HIGHER PHYSICS RESOURCES GUIDE
Higher Physics Resources Guide
This resource guide has been produced in response to requests from staff who attended the NQ Sciences events at

Chemistry Safety Notes
Volume 3, Issue 2
March 2015
Chemistry Safety Notes is published by the Chemistry Dept. Safety Committee, written & edited by Debbie Decker, Safety Mgr.
Spring!
Self/Peer Inspections Done!
Now that warmer weather has arrived, a chem

Sample manuscript for Journal of Chemical Physics
A. Author,1,2,a) B. Author,2,b,c) and C. Author3,c)
1
Department, University, City, Postal code, Country
2
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3
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Note
BULLETIN OF THE
KOREAN CHEMICAL SOCIETY
www.bkcs.wiley-vch.de
Aaa Author et al.
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to the Bulletin of the Korean Chemical Society (2015)
* Instruction for Using Template *
Please use Notes template for submission to the

MATERIAL SAFETY DATA SHEET
FILE NO.:
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Chapter 1 Review of Straight Lines
1.1
Find the slope and y intercept of the following straight lines: (a) y = 4x 5 (b) 3x 4y = 8 (c) 2x = 3y (d) y = 3 (e) 5x 2y = 23 Detailed Solution: (a) This is the slope-intercept equation for the line. The slope is 4

Chapter 4 Problems
37. Iron ore is impure Fe2O3. When Fe2O3 is heated with an excess of carbon (coke) , iron metal and carbon monoxide are produced. From a sample of ore weighing 938 kg, 523 kg of pure iron is obtained. What is the % Fe2O3 by mass in the

Math 102 Section 102 Midterm exam 2
Friday, 5 November 2009
Name (rst and last): SOLUTIONS
Student number:
1. Ensure that your full name and student number appear on this page. 2. No calculators, books, notes, or electronic devices of any kind are permitt