Temperature Dependent In-class Example
The decomposition of KClO3 is catalyzed by
MnO2:
MnO2
2 KClO3 2 KCl + 3 O2
The rate constant for the uncatalyzed reaction,
kuncat, measured at 100C, is 4.3x10-6 M-1 s-1.
If the catalyzed reaction decreases the
activa
SECTION 1.5
Exponential Functions and Models
Exponential functions are some of the most common functions used to model data. An exponential function can be described
in terms of a starting point and a multiplier applied at regular input intervals. The out
SECTION 1.6
Models in Finance
Savings, investments, trust funds, car loans, and mortgages are functions that deal with the value of money over time. Many
functions with nancial applications are exponential functions or are constructed from an exponential
SECTION 1.7
Constructed Functions
New functions can be created by combining known functions using addition, multiplication, subtraction, or division. Sometimes new functions can also be constructed using function composition or by nding the inverse of a f
SECTION 1.8
Logarithmic Functions and Models
1 Characteristic Behavior of Logarithmic Functions
In your precalculus class, you (should have) learned about logarithms: how they are dened, how they behave (based on
certain log properties), and how they are
SECTION 1.9
Quadratic Functions and Models
Quadratic functions form the third family of functions that we will discuss this semester that exhibit only a single type of
concavity over the entire input interval. Quadratic functions dier from exponential and
SECTION 1.10
Logistic Functions and Models
Although exponential models are common and useful, it is sometimes unrealistic to believe that exponential growth can
continue forever. In many situations, forces ultimately limit growth. In this case a logistic
SECTION 1.11
Cubic Functions and Models
Many dierent appearances of scatter plots of data can be reasonably modeled using a cubic function; however, they all have
one thing in commonthe presence of an obvious inection point.
1 Characteristic Behavior of C
SECTION 2.1
Measures of Change over an Interval
One of the primary goals of calculus is to measure change that is occuring at a point. In preparation for understanding how
calculus is used to describe instantaneous rate of change, we discuss three ways of
SECTION 2.2
Measures of Change at a PointGraphical
The average rate of change of a quantity is a measure of the change in that quantity over a specied interval. The change
occuring at a specic point can also be measured. One measure of the change of a qua
SECTION 2.3
Rates of ChangeNotation and Interpretation
1 Average Rate of Change vs. (Instantaneous Rate of Change)
Average Rate of Change:
measures how rapidly (on average) a quantity changes over an interval
can be obtained by calculating the slope of
SECTION 2.4
Rates of ChangeNumerical Limits and Nonexistence
The rate of change of a function at a point is equivalent to the slope of the line tangent to a graph of that function at that
point. A rate of change can be estimated numerically by using limit
SECTION 2.5
Rates of Change Dened Over Intervals
The rate of change at a specic point on a function can be represented as the limiting value of the slopes of secant lines
through that point and a series of close points. This limit of slopes can be general
SECTION 2.6
Rate-of-Change Graphs
1 Rate-of-Change Information from Function Graphs
Suppose you are given the graph of a function f (x). At each point where the graph is smooth and continuous, we could
draw the tangent line and estimate its slope. Thus, a
SECTION 3.1
Simple Rate-of-Change Formulas
Recall the limit denition of the derivative:
f (x + h) f (x)
h
In Section 2.5, we used this limit denition to calculate the derivative of certain functions. You probably recall how tedious
these calculations were
SECTION 1.4
Linear Functions and Models
Linear functions are often used to model situations in the real world. A linear function can be described in terms of a starting
point and a value added at regular input intervals. The output of a linear function ch
SECTION 1.3
Limits and Continuity
The use of limits to describe change sets calculus apart from algebra. In Section 1.2, limits are used to describe end behavior
of a function. Limits can also be used to describe the behavior of a functions output as the
SECTION 1.2
Function Behavior and End Behavior Limits
The behavior of real-world functions is often described verbally using conversational language such as growth, increase, and
decrease.
Lower private health insurance premium growth is expected over the
Chem 1415 Spring 2013
Dr. T. Martyn, Dept. of Chem. & Biochem., University of Oklahoma
In-class Example: Manipulating Equilibrium Constants
Unit 2 In-class Solutions
CHEM 1415
Spring 2013
Dr. T. Martyn
A.
B.
C.
D.
E.
In-class Example: Manipulating Equilib
Chem 1415 Spring 2013
Dr. T. Martyn, Dept. of Chem. & Biochem., University of Oklahoma
In-class Examples: Dissociation Reactions
Acetic acid (CH3COOH)
acid
Unit 3 In-class Examples
base
CH3COOH + H2O CH3COO- + H3O+
base
CHEM 1415
Dr. T. Martyn
Spring 2013
Chem 1415 Spring 2013
Dr. T. Martyn, Dept. of Chem. & Biochem., University of Oklahoma
In-class Example: Using the H-H Equation
A 1.0 L solution is initially prepared to contain 0.12 M
NH4Cl . After preparation, 0.10 moles of NaOH are
added to the solutio
DO NOT TURN THIS PAGE UNTIL DIRECTED TO DO SO
Chemistry 1415
EXAM 1
Spring 2007
Name _
Lab Instructor_
ID Number _
1. These tests are machine graded; therefore, be sure to use a No. 1 or 2 pencil for marking the answer sheets. Completely
blacken the answe
DO NOT TURN THIS PAGE UNTIL DIRECTED TO DO SO
Chemistry 1415
EXAM 1
Fall 2007
Name _
Lab Instructor_
ID Number _
1. These tests are machine graded; therefore, be sure to use a No. 1 or 2 pencil for marking the answer sheets.
Completely blacken the answer
DO NOT TURN THIS PAGE UNTIL DIRECTED TO DO SO
Chemistry 1415
EXAM 1
Spring 2008
Name _
Lab Instructor_
ID Number _
1. These tests are machine graded; therefore, be sure to use a No. 1 or 2 pencil for marking the answer sheets.
Completely blacken the answe
DO NOT TURN THIS PAGE UNTIL DIRECTED TO DO SO
Chemistry 1415
EXAM 1
Fall 2008
Name _
Lab Instructor_
ID Number _
1. These tests are machine graded; therefore, be sure to use a No. 1 or 2 pencil for marking the answer sheets.
Completely blacken the answer
DO NOT TURN THIS PAGE UNTIL DIRECTED TO DO SO
Chemistry 1415
EXAM 1
Spring 2009
Name _
Lab Instructor_
ID Number _
1. These tests are machine graded; therefore, be sure to use a No. 1 or 2 pencil for marking the answer sheets.
Completely blacken the answe
DO NOT TURN THIS PAGE UNTIL DIRECTED TO DO SO
Chemistry 1415
EXAM 1
Fall 2009
Name _
Lab Instructor_
ID Number _
1. These tests are machine graded; therefore, be sure to use a No. 1 or 2 pencil for marking the answer sheets.
Completely blacken the answer
DO NOT TURN THIS PAGE UNTIL DIRECTED TO DO SO
Chemistry 1415
EXAM 1
Spring 2010
Name _
Lab Instructor_
ID Number _
1. These tests are machine graded; therefore, be sure to use a No. 1 or 2 pencil for marking the answer sheets.
Completely blacken the answe
FORM A
Math 1743 Fall 2012 Exam I
Name: Section #:
i.d.#: Instructor:
Read all questions carefully and answer them completely. Show appropriate work to receive
maximum credit. In general, if you can label something with units, you should label it wi