Algebraic Manipulation of Limits
When direct substitution fails
Strategy 1: Factoring
Strategy 2: Rationalizing (conjugate multiplication)
Strategy 3: Combining fractions (complex fractions)
Strategy 4: Common factor in transcendental expressions
Decision flowchart
Strategy comparison
Additional worked example: factoring a cubic
Another example: double conjugate
Common mistakes
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Vocabulary
Unit 1 topics
Unit 1 overview11.1 Introducing Calculus: Can Change Occur at an Instant?21.2 Defining Limits and Using Limit Notation31.3 Estimating Limit Values from Graphs41.4 Estimating Limit Values from Tables51.5 Determining Limits Using Algebraic Properties61.6 Determining Limits Using Algebraic Manipulation71.7 Selecting Procedures for Determining Limits81.8 Determining Limits Using the Squeeze Theorem91.9 Connecting Multiple Representations of Limits and Continuity101.10 Types of Discontinuities, Infinite Limits, and the IVT