Chapter 2 of 10All chapters
Chapter 2 of 10
Limits
Getting arbitrarily close.
The idea
A limit is the value a function heads towards as the input approaches a point, whether or not it ever arrives. It makes dividing by ever smaller intervals meaningful.
- A function can have a limit at a point where it is not even defined.
- Limits also describe behaviour as inputs grow without bound.
Why it was needed
Newton and Leibniz used infinitely small quantities that worked but made no logical sense. Limits, two centuries later, made the same results rigorous.