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Mathematics lessons for IB® Diploma Programme

Analysis and Approaches | Calculus

To infinity and beyond


  • Develop an understanding of what it means to take a limit “at” infinity.
  • Develop an understanding of behavior that prevents limits from occurring by means of chaos or oscillation.
  • Estimate limits from graphs and tables of values.
  • Connect the ideas of end behavior, horizontal asymptotes, and limits at infinity.
  • Students will try to make a connection with how to understand these topics in IB Mathematics courses and on their final assessments.


  • Limits
  • Infinity
  • Asymptote

About the lesson

This activity has three parts. First, students will examine, graphically and numerically, the behavior of functions as the input approaches infinity. Next, they will examine graphically limits that do not exist because of continued chaotic output behavior as the input values continue to approach a particular value. Finally, students will examine a variety of limit problems.

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