Limits

The notes move from the formal meaning of approaching a value to the algebraic tools used in calculations.

Step	Question	Note
1	What does it mean for a function to approach a value?	Limit Definitions
2	When does a two-sided limit exist?	Two-Sided and One-Sided Limits
3	Which algebraic operations preserve limits?	Limit Laws
4	Which standard patterns are worth recognizing?	Common Limit Patterns
5	How should an indeterminate expression be transformed?	Evaluating Limits
6	When does nearby behavior agree with the function value?	Continuity

External references: Paul's Online Notes and the CLP-1 differential calculus text.

The scope is real-valued functions of one real variable: finite and infinite limits, elementary calculation, and pointwise continuity. Assume familiarity with function domains, inequalities, absolute value, factoring, and radians. Sequence convergence and uniform continuity are outside this introduction. The next step is the derivative as a limit.

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