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References: Evaluating Limits

  1. Limit of a function - Wikipedia - Covers algebraic techniques for evaluating limits including factoring, rationalization, and standard limit results used throughout this chapter.

  2. Squeeze theorem - Wikipedia - Rigorous statement and proof of the squeeze theorem with visual illustrations. Directly supports the squeeze theorem technique taught in this chapter.

  3. Indeterminate form - Wikipedia - Classifies the seven indeterminate forms and explains why direct substitution fails in each case. Essential background for the limit evaluation strategies in this chapter.

  4. Calculus: Early Transcendentals (9th Edition) - James Stewart - Cengage Learning - Sections 2.3-2.5 cover limit laws, the squeeze theorem, and algebraic evaluation techniques with extensive worked examples.

  5. Calculus (11th Edition) - Ron Larson, Bruce Edwards - Cengage Learning - Chapter 1.3 provides a systematic approach to evaluating limits algebraically with clear decision trees for choosing techniques.

  6. Evaluating Limits - Paul's Online Math Notes - Detailed walkthrough of direct substitution, factoring, rationalizing, and combining fractions with step-by-step solutions.

  7. Limit Laws and Techniques - Khan Academy - Practice problems on applying limit properties and algebraic manipulation, with immediate feedback aligned to AP curriculum.

  8. Special Trigonometric Limits - Paul's Online Math Notes - Covers the fundamental trig limits sin(x)/x and (1-cos(x))/x with geometric proofs and applications.

  9. The Squeeze Theorem - Math is Fun - Accessible visual explanation of the squeeze theorem with interactive examples that complement the chapter's MicroSim.

  10. Limit Evaluation Techniques - Whitman College Calculus - Open-source textbook section with clean explanations of limit evaluation methods and self-check exercises.