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Chapter 1.6
Finding limits algebraically - when direct substitution is not possible
What You'll Learn
Apply algebraic techniques when direct substitution produces undefined forms
Factor polynomials to cancel common terms and eliminate zero denominators
Rationalize expressions using conjugates to remove square roots
Use trigonometric limit formulas for sine and other trig functions
Evaluate piecewise functions by considering left and right limits separately
What You'll Practice
1
Factoring difference of squares to simplify rational functions
2
Expanding and canceling terms in polynomial limit expressions
3
Multiplying by conjugates to rationalize denominators with radicals
4
Applying the sine theta over theta limit formula with variable substitution
5
Evaluating limits of absolute value functions from both directions
Why This Matters
Mastering algebraic limit techniques is essential for calculus success. These methods help you evaluate complex limits that appear throughout derivatives, integrals, and advanced applications, making them fundamental tools you'll use in every calculus course and beyond.
This Unit Includes
5 Video lessons
Practice exercises
Skills
Limits
Factoring
Conjugates
Rationalization
Trigonometric Limits
Piecewise Functions
One-Sided Limits
Indeterminate Forms
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