Calculus I
(Lecture 12 & Lab #12)
Applications of Differentiation [Part 3]
Ziad Z. Adwan
()
Lecture 12 & Lab 12
1 / 36
Learning Objectives
1
Monotone Functions & the 1st Derivative Test .
Motivation for & Denition of Monotone Functions.
Test for Increasin
Calculus I
(Lecture & Lab #9)
Exponential & Logarithmic Functions
Ziad Z. Adwan
()
Lecture & Lab 9
1 / 39
Learning Objectives
1. Exponential Functions.
Denition, Graph, & Properties of Exponential Functions.
The Denition of the Number e and where it comes
Calculus I
(Lecture 11 & Lab #11)
Applications of Differentiation [Part 2]
Ziad Z. Adwan
()
Lecture 11 & Lab 11
1 / 26
Learning Objectives
1
The Mean Value Theorem (MVT) .
Motivation for the Mean Value Theorem.
Rolle Theorem:
s
A Proof using the Extreme-V
Calculus I
(Lecture & Lab #10)
Applications of Differentiation [Part 1]
Ziad Z. Adwan
()
Lecture & Lab 10
1 / 23
Learning Objectives
1. Extrema on an Interval & the Extreme Value Theorem .
Denition of Extrema of a Function on an Interval.
Denition of Abso
Calculus I
(Lecture #8)
Rules for Computation of Derivatives [Part 3]
Ziad Z. Adwan
()
Lecture 8
1 / 30
Learning Objectives
1. The Chain Rule.
Motivation for the Chain Rule.
How to Find Derivatives of Composite Functions.
2. Implicit Dierentiation.
Unders
Calculus I
(Lecture #5)
Introduction to the Derivative of a Function
Ziad Z. Adwan
()
Lecture 5
1 / 26
Learning Objectives
1. The Tangent Line Problem [Revisited].
2. Denition of the Derivative at a Point and in General.
3. Computing the Derivative at a P
Calculus I
(Lecture #7)
Rules for Computation of Derivatives [Part 2]
Ziad Z. Adwan
()
Lecture 7
1 / 23
Learning Objectives
1. The Product Rule.
2. The Quotient Rule.
3. Derivatives of Trigonometric Functions.
4. Higher Order Derivatives.
5. Rates of Chan
Calculus I
(Lecture #6)
Rules for Computation of Derivatives [Part 1]
Ziad Z. Adwan
()
Lecture 6
1 / 20
Learning Objectives
1. The Constant Rule.
2. The Power Rule.
3. The Constant Multiple Rule.
4. The Sum and Dierence Rules.
5. Derivatives of Sine and C
Calculus I
(Lecture #2)
Limits of Functions
Ziad Z. Adwan
()
Lecture 2
1 / 20
Learning Objectives
1. Understanding the Concept of a Limit.
2. Limits which Fail to Exist.
3. Rules for Computing Limits.
4. Limits Involving Innity & Asymptotes.
Ziad Z. Adwan
Calculus I
(Lecture #1)
Preparation for Calculus
Ziad Z. Adwan
()
Lecture 1
1 / 10
Learning Objectives
1. The Tangent Line Problem
2. The Area Problem.
3. Lengths of Curves.
Ziad Z. Adwan
()
Lecture 1
2 / 10
The Tangent Line Problem
Ziad Z. Adwan
()
Lectu
Domain of composite function example:
Domain for : Step 1 Domain for is all x so that x + 10
So we need .
Step 2 Output for g becomes input for f so we must find the range of g.
Graph g to see that range of g is . Step 3 Find domain of f. All x so that
Th
Notes for Section 5.6
Find a polynomial of degree 6 whose coefficients are real numbers and has the zeros 2, -3, 2i,
1-2i.
By the Conjugate Pairs Theorem, since 2i is a zero, then -2i is too and since 1 2i is a zero,
then 1 + 2i is as well. This gives us
Notes for Section 5.5
Using the function , we apply the material in the section.
Bounds on real zeros: means (1) first divide all coefficients by the leading coefficient to get x4
+(1/2)x3 (7/2)x2 (3/2)x + (3/2)
Now find the bound. Choose the largest of t
Calculus I
Preface
Here are the solutions to the practice problems for my Calculus I notes. Some solutions will have
more or less detail than other solutions. The level of detail in each solution will depend up on
several issues. If the section is a revie
Preface
Here are my online notes for my Calculus I course that I teach here at Lamar University. Despite
the fact that these are my class notes, they should be accessible to anyone wanting to learn
Calculus I or needing a refresher in some of the early to
Preface
Here are my online notes for my Calculus I course that I teach here at Lamar University. Despite
the fact that these are my class notes, they should be accessible to anyone wanting to learn
Calculus I or needing a refresher in some of the early to
Calculus I
Preface
Here are the solutions to the practice problems for my Calculus I notes. Some solutions will have more or less detail than other solutions. The level of detail in each solution will depend up on several issues. If the section is a revie
Preface
Here are my online notes for my Calculus I course that I teach here at Lamar University. Despite the fact that these are my class notes they should be accessible to anyone wanting to learn Calculus I or needing a refresher in some of the early top
Preface
Here are the solutions to the practice problems for my Calculus I notes. Some solutions will have more or less detail than other solutions. The level of detail in each solution will depend up on several issues. If the section is a review section,
Preface
Here are my online notes for my Calculus I course that I teach here at Lamar University. Despite
the fact that these are my class notes, they should be accessible to anyone wanting to learn
Calculus I or needing a refresher in some of the early to
Preface
Here are the solutions to the practice problems for my Calculus I notes. Some solutions will have more or less detail than other solutions. The level of detail in each solution will depend up on several issues. If the section is a review section,
Preface
Here are my online notes for my Calculus I course that I teach here at Lamar University. Despite the fact that these are my class notes they should be accessible to anyone wanting to learn Calculus I or needing a refresher in some of the early top