The Limit of a Function

Section 1.5 in Stewart's Calculus.

Preclass Learning Objectives:

  • The limit at an x-value describes the y-value the function “approaches” at that x-value.
  • Graphical intuition for limits.
  • Two-sided limits depend on both one-sided limits.

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Tangents, Derivatives, and Rates of Change


Section 1.4/2.1 in Stewart's Calculus.

Preclass Learning Objectives:

  • A rate of change describes how one quantity changes in relation to another quantity.
  • Rate of change can result from averaging over an interval or finding a limit of averages approaching a single point.
  • Tangent lines result from the limit of secant lines.
  • A derivative is an instantaneous rate of change.

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Limit Laws


Section 1.6 in Stewart's Calculus.

Preclass Learning Objectives:

  • Algebraic limit laws.
  • When direct substitution isn't allowable in calculating a limit try simplification, conjugation, or squeezing the function.

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Continuity


Section 1.8 in Stewart's Calculus.

Preclass Learning Objectives:

  • Graphical intuition of continuity.
  • Where limits align with actual values, a function is continuous.
  • Types of discontinuities.
  • Algebraic limit laws.
  • Continuous functions cannot jump (Intermediate Value Theorem).

Classroom Slides PDF