Infinite Limits

When developing intuition and skills for how graphs behave toward infinity, there is really no substitute for having the class get their hands dirty in graphing practice. This problem set with accompanying presentation and homework on infinite limits does just that. Functions are carefully chosen to emphasize different graph behaviors and characteristics, without getting bogged down in messy arithmetic. A great resource to add to your repetoire on graphing limits and determining asymptotic behavior.

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CCSS: Adaptable
Instructional Ideas

  • Consider using in a flipped classroom model as classwork after reading or viewing an infinite limit assignment at home
  • Break down homework sheet into individual problems and use for remediation or bell ringer review problems
  • Link to number theory by including a discussion of the cardinality of infinity, and different sizes of infinity
Classroom Considerations

  • Note that the attached homework sheet does not include sufficient space between problems for showing work
  • Class notes and homework to match main resource presentation are available under included materials
  • Presentation PDF would work well on an interactive whiteboard by revealing solution steps and graphs in turn
  • Useful to have on hand for reviewing infinite limits in a calculus class prior to introducing L'Hopital's rule
Pros

  • Multiple examples of each type of function and behavior
  • Clearly scaffolded problems increase in difficulty as skills grow
  • Answer key included for homework
  • Problems from notes worked step-by-step in presentation
Cons

  • Notes ask analysis questions related to drawing conclusions about functional behavior that are not covered in the presentation provided
  • No included resources for teaching methods