How to Prove that the Limit Does Not Exist

Can you prove a negative? In watching the video, individuals learn how to prove that the limit of a function does not exist at a point. The video covers the quintessential example of the limit of f(x) = abs(x)/x as x approaches 0.

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Concepts

Instructional Ideas

  • Have the class graph the function in the example to visually confirm that the limit does not exist
Classroom Considerations

  • Learners must have experience with step functions
  • Pupils should already understand the existence of limits in terms of the one-sided limits
Pros

  • Shows work in an orderly fashion
  • Thoroughly explains each step before moving on to the next one 
Cons

  • Slight inaccuracies