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White Crane Education

Introduction to Calculus

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Limits and Continuity

Introduction
A Heuristic Definition
A Formal Definition
Methods and Techniques
Left/Right Limits
Limits at Infinity
Continuity

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Differentiation

Introduction
The Derivative as the Rate of Change
The Derivative as a Function
Differentiation Properties and Formulas
The Product and Quotient Rules
The Chain Rule
Implicit Differentiation
Derivatives of Logarithmic and Exponential Functions
Derivatives of Inverse Trigonometric Functions
Hyperbolic Functions

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Applications of Differentiation

Introduction
The Derivative as the Rate of Change
Indeterminate Forms and L'Hôpital's Rule
Maximum and Minimum Values
Concavity and Curve Sketching
Optimization
Related Rates

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Introduction
Antiderivatives
Indefinite Integrals and Integration by Substitution
Areas and Finite Sums
Definite Integrals
The Fundamental Theorem of Calculus
Area between Curves
Separable Differential Equations

Introduction Topics: Introduction

Chapter 1: Limits and Continuity

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