**UNIT 1: LIMITS AND CONTINUITY**- 1.1 Introduction: Solving Limit of a Function
- 1.2 Different Techniques on Solving Limits
- 1.3 Evaluating Limit Given the Graph of the Function
- 1.4 Solving Infinite Limit and One-Sided Limit
- 1.5 Limit at Continuity
**UNIT 2: DERIVATIVES**- 2.1 Definition of Derivatives
- 2.2 Derivative Rule: Power and Constant Rules
- 2.3 Practice Exercises on Power and Constant Rules
- 2.4 Quotient Rule
- * 2.5 Computing for the Tangent Line of a Function at a Given Point
- 2.6 Product Rule
- 2.7 Chain Rule
- 2.8 Practice Exercises on Using Chain Rule
- 2.9 Differentiating Trigonometric Functions
- 2.10 Practice Exercises on Using Derivatives of Trig. Functions
- 2.11 Differentiating the Inverse of Trigonometric Functions
- 2.12 Derivatives – Exponential Functions (e and constant)
- 2.13 Derivative ng Logarithmic at Ln Functions
- 2.14 Practice Exercises on Using Derivative Rule of Logarithmic Functions
- 2.15 Derivative Rule of Transcendental Functions
**UNIT 3: APPLICATIONS OF DERIVATIVES**- 3.1 Writing the Tangent Line of a Function at a Point
- 3.2 Using the Derivative Rules in Differentiating Functions
- 3.3 Finding the Derivative of a Function Given its Table of Values
- 3.4 Implicit Differentiation
- 3.5 Higher Order Derivative Using Implicit Differentiation
- 3.6 Solving Related Rates Problems on Circle and Balloons
- 3.7 Solving Related Rates Problems on Cones and Ladder
- 3.8 Practice Exercises on Related Rates
- 3.9 Solving Word Problems on Optimization
- 3.10 Practice Exercises on Solving Optimization Problems
- 3.11 Using Derivatives in Solving Problems on Rectilinear Motion
**UNIT 4: INTEGRATION**- 4.1 Computing for Antiderivative of a Function
- 4.2 Solving Area Under the Curve Using Reimann Sums
- 4.3 Solving Area Under the Curve Using Reimann Sums with Graphing Calculator
- 4.4 Applications of Reimann Sums in Approximating Distance Traveled
- 4.5 Evaluating Definite Integrals
- 4.6 Properties of Integration and Absolute Value Integration
- 4.7 Fundamental Theorem of Calculus and Integration Using Substitution Method
- 4.8 Application of Definite Integral in Solving Problems in Motion
- 4.9 Solving Area Between Curves
- 4.10 Solving Area Using Subregions
- 4.11 Evaluating Differential Equations
- 4.12 Solving Separable Differential Equations
**UNIT 5: ENRICHMENT**- 5.1 Mean Value Theorem
- 5.2 Rolle's Theorem
- 5.3 Extreme Value Theorem
- 5.4 First Derivative Test: local extrema and direction of function
- 5.5 Second Derivative Test: Concavity and Point of Inflection
- 5.6 Solving Volumes of a Solid Rotated on an Axis: Disk Method
- 5.7 Solving Volumes of a Solid Rotated on an Axis:WASHER method
- 5.8 Computing for Volumes using Known Cross-Section
- 5.9 Integration Using the U-Substitution Method
- 5.10 Analyzing the graph of f(x) Using the derivative graph: f'(x)