AP Calculus Book 1: Limits, Continuity, and Differentiation

Build a Strong Foundation for Calculus Success

AP Calculus Book 1: Limits, Continuity, and Differentiation provides a comprehensive introduction to the core concepts of calculus. This book is designed to help students grasp essential topics, preparing them for the AP Calculus exam with clear explanations, practice exercises, and real-world applications.

Understanding Limits and Continuity

The book begins by explaining the concept of limits, including one-sided limits, infinite limits, and limits at infinity. First, students learn techniques for evaluating limits and understanding their significance in calculus. Next, the book covers continuity, exploring what it means for a function to be continuous and the consequences of discontinuities.

Introduction to Differentiation

In addition, the book introduces differentiation, explaining the derivative and its geometric interpretation as the slope of a tangent line. Students learn rules of differentiation for algebraic, trigonometric, exponential, and logarithmic functions. Furthermore, higher-order derivatives and their applications are discussed to deepen understanding.

Applications and Problem-Solving

The book emphasizes applying derivatives to real-world problems, including rates of change, optimization, and curve sketching. Moreover, step-by-step examples and practice problems reinforce learning and build problem-solving skills necessary for AP exam success.

Exam Preparation

AP Calculus Book 1 includes practice exercises, chapter summaries, and review questions to simulate the exam environment. Additionally, students can assess their progress, identify weaknesses, and strengthen their understanding of limits, continuity, and differentiation.

Whether you are starting calculus for the first time or preparing for the AP exam, AP Calculus Book 1: Limits, Continuity, and Differentiation is an essential resource for mastering foundational calculus concepts.