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Lesson Packs · Grade 12 · Mathematics

Limits at Infinity and Asymptotes

Students evaluate limits at infinity by dividing by the highest power and by comparing degrees, find infinite one-sided limits, and use both to identify vertical, horizontal and oblique asymptotes from equations and graphs.

MathematicsGrade 12Unit 1 · Lesson 2G12-MAT-02
Slide 1
Limits at Infinity and Asymptotes — Slide 1
+34in the download
39slides: lesson, examples and worksheet
11worksheet questions
34marks in total
4 + 5worksheet + answer key pages

Learning objectives

  • Evaluate limits of rational functions as x → ∞ and x → −∞ by dividing by the highest power of x or by comparing degrees.
  • Find infinite one-sided limits and describe how a function behaves near a vertical asymptote.
  • Identify vertical, horizontal and oblique asymptotes from an equation or a graph.

What's inside

  • 39 PowerPoint slides: lesson, worked examples and the worksheet with solutions
  • 11 worksheet questions (34 marks) with step-by-step solutions
  • Printable worksheet (4 pages) and a teacher answer key
  • Fully editable in PowerPoint, Google Slides, Keynote and Word

More lessons in Unit 1

All Grade 12 Mathematics lessons

Questions teachers ask

Can I edit the files?

Yes. The PowerPoint and the Word worksheet are fully editable, so you can change examples, add questions or adapt the design for your class.

How do I use the worksheet slides?

After the teaching slides, each worksheet question appears on its own slide. Let students try it first, then show the next slide and work through the solution together.

Is there an answer key?

Yes. The Word file ends with a teacher answer key that has the answer and a worked solution for every question. It is also included as a separate PDF.

Which languages are available?

Every Lesson Pack is made in 18 languages: English, Simplified Chinese, Hindi, Spanish, Arabic, French, Bengali, Portuguese, Indonesian, Urdu, Vietnamese, Albanian, Italian, German, Turkish, Malay, Greek and Traditional Chinese (Hong Kong).

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