Famous Limits

sin x / x and infinity

An interactive lesson with 7 steps, about 6 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• $\lim_{x \to 0} \frac{\sin x}{x} = 1$, proved by the squeeze theorem.
• At infinity, compare the leading terms.
• Exponentials outgrow every power.

Steps

1. sin x over x
2. The squeeze
3. Three shapes, one limit
4. Compound interest
5. A stretched sine
6. Wild oscillation
7. Which wins?