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Accepted Answer

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Question 2

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Accepted Answer

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Question 3

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Accepted Answer

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Question 4

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Accepted Answer

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Question 5

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Accepted Answer

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Course Outline

Introduction to Functions: Definition, Types, and Graphs

The Epsilon-Delta Definition of a Limit

One-Sided Limits: Left-Hand and Right-Hand Limits

Continuity: Types and Theorems

Intermediate Value Theorem

Derivatives: Definition and Geometric Interpretation

Rules of Differentiation: Power, Product, and Quotient Rules

Applications of Derivatives: Tangent Lines and Rates of Change

Higher-Order Derivatives and their Applications

Introduction to Related Rates and Optimization Problems

Functions and their Notations

Types of Functions: Linear, Quadratic, Polynomial

Rational Functions

Exponential Functions

Logarithmic Functions

Trigonometric Functions

Inverse Functions

Composite Functions

Piecewise Functions

Transformations of Functions

Domain and Range of Functions

Basic Function Properties

End Behavior of Functions

Symmetry in Functions

Periodic Functions

Limits at Infinity

Squeeze Theorem

Limit Properties

Continuity Definition

Types of Discontinuities

Evaluating Limits Analytically

Finding Limits Graphically

Vertical and Horizontal Asymptotes

The Derivative as a Limit

Derivative Notation

Interpretation of the Derivative

Tangent Lines and Secant Lines

Rules of Differentiation: Power Rule

Rules of Differentiation: Product Rule

Rules of Differentiation: Quotient Rule

Rules of Differentiation: Chain Rule

Implicit Differentiation

Derivatives of Trigonometric Functions

Derivatives of Exponential Functions

Derivatives of Logarithmic Functions

Rate of Change

Applications of Derivatives: Tangent and Normal Lines

Optimization Problems

Related Rates

Critical Points

First Derivative Test

Second Derivative Test

Concavity and Inflection Points

Graphing Functions with Derivatives

Mean Value Theorem

Rolle's Theorem

L'Hôpital's Rule

Continuous Functions and Their Limits

Using Calculators for Derivatives

Graphing Calculators: Function Plotting

Software Tools for Calculus

Interpreting Graphs of Functions

Mathematical Modeling with Derivatives

Piecewise Derivatives

Understanding Limits with ε-δ Definitions

Derivative Applications in Physics

Velocity and Acceleration

Economic Applications of Derivatives

Understanding Marginal Cost and Revenue

Biological Applications of Derivatives

Velocity and Acceleration in Natural Contexts

Using Derivatives to Model Real-World Situations

Graphical Interpretation of Derivatives

Velocity and Position Functions

Applications in Environmental Science

Applications of Limits in Engineering

Statistical Applications in Calculus

Maxima and Minima Problems

Shape Optimization with Derivatives