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Getting Close — Limits Preview

Overview

What does it mean to approach a value without reaching it? This question defines limits — and limits define derivatives and integrals.

Key Concepts

1

"x → 2" means: x gets arbitrarily close to 2, but need not equal 2

2

Approach from the left: x → 2⁻ (values like 1.9, 1.99, 1.999…)

3

Approach from the right: x → 2⁺ (values like 2.1, 2.01, 2.001…)

4

If both sides agree on the same value, the limit exists

See it in action

Use the interactive visualizer to explore this concept with real graphs.

Open Limits Explorer