Understanding the Concept of a Limit

This animation shows a point moving along a function's graph as its input approaches a fixed value, tracking how the output values converge toward a specific number even if the function is undefined there. A zoom-in effect highlights the narrowing gap between input and target, reinforcing the idea of approaching without necessarily reaching. Useful for students beginning calculus who need an intuitive, visual grounding before working with formal limit definitions and notation.

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The prompt that made it

Visualization of Limit concept

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• Show the epsilon-delta definition of a limit with adjustable tolerance bands
• Visualize one-sided limits approaching from left and right separately
• Demonstrate a limit that does not exist due to oscillating behavior

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