Theorem
Unit 3.3
Theorems on
Differentiation
Theorem
Example 3.3.1
Theorem
1
Theorem
Example 3.3.2
Product Rule
Example 3.3.3
Example 3.3.4
Quotient Rule
2
Example 3.3.5
Example 3.3.6
Theorem
Required Exercises
3
End of Chapter 3.3
4
MATH 36 B
Recitation Class
January 7, 2014
Definition:
For any real number x , x n if n x n 1 . That is, x is the greatest
integer less than or equal to x .
For instance, 1 1 , 1.3 1 , 0.5 0 , 4.2 5 , and 8 8 .
Example 1:
Find lim x .
Solution:
For lim x
Absolute Extrema
Unit 4.5
Optimization
Extreme Value Theorem
Finding Absolute Extrema
on Closed Intervals
Example 4.5.1
1
Theorem
Finding Absolute Extrema
on Open Intervals
Example 4.5.2
2
Example 4.5.3
Steps in Solving Optimization Problems
3
Example 4.5
Unit 2.2
One-Sided Limits
Right-Hand Limit
1
Left-Hand Limit
Example 2.2.1
Example 2.2.2
Example 2.2.3
2
Example 2.2.4
Required Exercises
End of Unit 2.2
3
Sequences
Unit 2.5
Sequences of Real
Numbers
Terms/Elements
Definition of a Sequence
1
Example 2.5.1
Example 2.5.2
Graph of a Sequence
Example 2.5.3
2
Limit of a Sequence
Convergent and Divergent Sequences
Example 2.5.4
3
Theorem
Example 2.5.3
4
End of Un
Unit 2
Limits and Continuity
Unit 2.1
Limit of a Function
1
Example 2.1.1
Limit of a Function
Proving Limits of a Function
Example 2.1.2
2
Example 2.1.3
Challenge!
Theorem
Theorem
3
Example 2.1.4
Theorem
Example 2.1.5
4
Required Exercises
End of Chapter 2
Challenge
Unit 1.4
General Second-Degree
Equations
Conic Sections
General Second-Degree Equations
1
Theorem
Example 1.4
2
Required Exercises
End of Unit 1.4
3
Unit 2.4
Limits at Infinity
Limit at Infinity
Limit at Infinity
Theorem
1
Example 2.4.1
Recall
Example 2.4.2
2
Reading Assignment
Required Exercises
End of Unit 2.4
3
Unit 1.5
Rotation of Axes
1
Theorem
Theorem
Second Degree Equations with xy Term
Example 1.5.1
2
Theorem
Example 1.5.2
3
Example 1.5.3
4
Required Exercises
End of Unit 1.5
5
Unit 2.6
Continuity of a Function
Continuity of a Function at a Number
Example 2.6.1
1
Example 2.6.2
Example 2.6.3
2
Example 2.6.4
Example 2.6.5
Example 2.6.6
3
Right-Hand Continuity
Left-Hand Continuity
Example 2.6.7
4
Theorem
Theorem
Example 2.6.8
Conti
Unit 2.3
Inifinite Limits
Function Values Increasing
Without Bound
Function Values Decreasing
Without Bound
Theorem
1
Theorem
Example 2.3.1
Reading Assignment
Required Exercises
2
End of Unit 2.3
3
Hyperbola
Unit 1.3
Hyperbola
1
Transverse Axis
2
Conjugate Axis
Center
3
Standard Equation
Graphing a Hyperbola
Example 1.3
4
5
6
Required Exercises
End of Unit 1.3
7
Ellipse
Unit 1.2
Ellipse
1
Major Axis
2
Minor Axis
Center
3
Standard Equation
Example 1.2.1
4
5
Real World Ellipses
6
Required Exercises
End of Unit 1.2
7
Relation
Unit 1
Conic Sections
Graph of a Relation
Line
1
Circle
Conic Section
Non-Degenerate Conics
2
Eccentricity
Principal Axis
Vertex
Unit 1.1
Parabola
3
Parabola
Latus Rectum
4
Length of the Latus Rectum
Example 1.1.1
5
Standard Equation
Example 1.1.
9/ 10/ 2011
4. 1 Unit Circle
Chapter 4
Circular and
Trigonometric Functions
A unit circle is a circle whose radius is equal to
one unit and whose center is at the origin.
Every point on the unit circle satisfies the
equation
x2 y2 1.
y
Example 4.1.1
1.5
1
9/ 27/ 2011
Types of E
quations
Chapter 4.6
Equations Involving C
ircular
and Inverse C
ircular Functions
Identit ies are satisfied by all values of the
unknown arc length for which the functions
are defined.
sin x csc x 1 is an identity.
Types of E
quati
January 15, 2014
To whom it may concern,
This is to certify that Nico C. Crisostomo is enrolled at Math 36 under Mr. Anthony L.
Cueno. Also, he is having his exam in Math 36 on January 22, 2014. Thus, he is requested to take
a special exam in his IT 1.
Th
Definite Integral
Unit 5.4
The Definite Integral
Properties of Definite Integral
Fundamental Theorem of Calculus I
1
Example 5.4.1
Example 5.4.2
Fundamental Theorem of Calculus II
Example 5.4.3
2
Required Exercises
End of Unit 5.4
3
Differentiable Function
Unit 3.2
Differentiability
and Continuity
Example 3.2.1
One-Sided Derivative
1
Example 3.2.2
Theorem
Theorem
Theorem
2
Cases where f is not Differentiable at a
Required Exercises
End of Unit 3.2
3
Unit 3
Differentiable Functions
Unit 3.1
Derivative of a Function
Slope of a Line
Derivative of a Function
1
Example 3.1.1
Example 3.1.2
2
Example 3.1.3
Required Exercises
End of Unit 3.1
3
MATH 36 B
RECITATION CLASS
MARCH 13, 2014
A differential equation is an equation that involves an unknown function and its derivatives.
A solution to a differential equation is a function that satisfies the equation.
Example.
Consider the differential equ
Rolles Theorem
Unit 3.7
Rolles Theorem and
Mean Value Theorem
Example 3.7.1
Example 3.7.2
1
Mean Value Theorem
Example 3.7.3
Example 3.7.4
Required Exercises
2
End of Unit 3.7
3
Squeeze Theorem
Unit 2.7
Limits and Continuity of
Trigonometric Functions
Example 2.7.1
Theorem
1
Theorem
Theorem
Theorem
Theorem
2
Example 2.7.2
3
Required Exercises
End of Unit 2.7
4
Unit 5
Integrable Functions
Unit 5.1
Antiderivatives
Antiderivatives
Example 5.1.1
General Antiderivative
1
Notation
Example 5.1.2
Example 5.1.3
Theorems
2
Example 5.1.4
Theorems
Example 5.1.5
3
Chain Rule
Example 5.1.6
4
Required Exercises
End of Unit 5.
Relative Extrema
Unit 4.4
Curve Sketching
Critical Number
Example 4.4.1
Example 4.4.2
1
Theorem
First Derivative Test
Example 4.4.3
2
Concavity
Theorem
Monotonicity and Concavity
Concave Upward
Concave Downward
Increasing
Decreasing
Second Derivative Test