Limit Explorer

Visualize limits graphically with epsilon-delta definition and discontinuity analysis

Overview

The Limit Explorer provides an interactive visualization of limits, one-sided limits, and the epsilon-delta definition. Explore continuity, various types of discontinuities, and asymptotic behavior graphically to build intuition about this fundamental calculus concept.

Tips

  1. Try direct substitution first when finding a limit - if it works without giving 0/0 or ∞/∞, you’ve found your answer
  2. Check one-sided limits separately at points of discontinuity to understand jump and removable discontinuities
  3. Use the epsilon-delta controls to interact with the formal definition and see how δ must change as you adjust ε
  4. Look for patterns in the table of values by examining what happens as x approaches the limit point from both directions
  5. Identify discontinuity types by comparing left and right limits: if equal but different from f(a), it’s removable; if unequal, it’s a jump discontinuity