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Adirondacks National Park

Calculus AB - Unit One

Limits

 

Many calculus concepts are developed by first considering a discrete model and then the consequences of a limiting case. Therefore, the idea of limits is essential for discovering and developing important ideas, definitions, formulas, and theorems in calculus. Students must have a solid, intuitive understanding of limits and be able to compute various limits, including one-sided limits, limits at infinity, the limit of a sequence, and infinite limits. They should be able to work with tables and graphs in order to estimate the limit of a function at a point. Students should know the algebraic properties of limits and techniques for finding limits of indeterminate forms, and they should be able to apply limits to understand the behavior of a function near a point. Students must also understand how limits are used to determine continuity, a fundamental property of functions.

Click on a link to jump ahead to the following sections:

  • Lessons
  • Other Resources


Limits

Lessons

  • Lesson 1: Rates of Change and Tangent Lines
    • Advantage In - complete lesson

  • Lesson 2: Introduction to Limits
    • Close Enough - complete lesson

  • Lesson 3: Calculating Limits
    • Limits - complete lesson

  • Lesson 4: Limits Involving Infinity
    • Limits Involving Infinity - complete lesson on Asymptotes and End Behavior
    • Video - NancyPi video on YouTube

  • Lesson 5: Continuity
    • Continuous Functions - complete lesson on Continuity

  • Lesson 6: Assessment
    • AP Practice - Multiple Choice problems from previous AP exams

  • Supplemental Tasks:
    • Blueberry Pancake Recipe with limits
    • Limits of Piecewise Functions - Try to evaluate the one-sided limits of the piecewise functions in the GeoGebra app below.





Resources - Limits

The following are links to resources for Limits:

  • Limits and Continuity - Entire unit on Khan Academy


  • Calculating Limits - A concise summary of the different methods used in evaluating limits


The following are other free resources:

  • GeoGebra - Free online math tools

  • Desmos - Free online graphing calculator







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