Finding Limits Using Tables and Graphs

An excellent set of problems for developing limit intuition in learners, this presentation and homework set leads the class from testing basic continuous functions through to discontinuous piecewise problems. Using both table and graphical methods, the emphasis throughout the work is on precision and the notation of limits (i.e. left hand, right hand, infinite, etc.). An approachable inroad into the world of differential calculus, these problems definitely help the young algebrist develop a higher level of mathematical sophistication.

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CCSS: Adaptable
Instructional Ideas

  • Use as a review presentation in a calculus class before introducing formal limit delta definitions
  • Great for a reteaching and remediation tool for learners struggling with limit concepts and notations
  • Problems that involve left and right limits can be split into two parts, solved by different groups who then come together to compare notes and decide on an overall limit
Classroom Considerations

  • Main resource presentation is accompanied by student notes, homework sheet, and homework key in the included materials
  • Presentation would work fabulously on an interactive whiteboard, with each solution revealed as the problem is worked
  • Good supplemental lesson to existing material on finding limits, but consists mainly of examples and not instructive material. It would make for a confusing stand-alone lesson on limits
  • Homework answer key written in pencil might not stand up to repeated copying 

  • Many included examples of all kinds of functions and limits
  • Careful treatment of rounding and precision when calculating left- and right-hand limits
  • Graphs are easily duplicated and clearly drawn

  • No teaching notes or methods suggested