Continuity

Drawing without lifting your pen

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• Continuous at $a$: $\lim_{x \to a} f(x) = f(a)$.
• Intermediate value theorem: a continuous function that changes sign must cross zero.
• Bisection uses this to trap a root, halving the interval each step.

Steps

1. No breaks
2. Hunting a root
3. How narrow?
4. Join the pieces
5. cos x = x
6. Opposite points