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Grade 12 Math Lab: Analysis & Inference FREE

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Limits and Continuity

65 min Grade 12 Math Lab: Analysis & Inference

Learning Objectives

  • Evaluate limits
  • Understand continuity
  • Apply epsilon-delta definition

Key Concepts

Limit

Value a function approaches

Continuity

No breaks, holes, or jumps

Theory

**Limit Notation:** lim(x→a) f(x) = L **Limit Laws:** - lim[f(x) + g(x)] = lim f(x) + lim g(x) - lim[f(x) · g(x)] = lim f(x) · lim g(x) - lim[f(x)/g(x)] = lim f(x) / lim g(x) (if limit of g ≠ 0) **Continuity at a point:** lim(x→a) f(x) = f(a)

Examples

lim(x→2) (x² - 4)/(x - 2)

Solution: Factor: (x+2)(x-2)/(x-2) = x+2 → 4

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Knowledge Check

Test your understanding of Limit Lens!