Limits and Derivatives.

12 lessons93 min2 simulations

This chapter opens calculus. The speed of a falling body at one instant cannot be read off as distance over time, so it is chased by averages over shorter and shorter intervals, and that chase is made exact by the idea of a limit. One-sided limits decide when a limit exists, limit rules and factor-cancelling handle polynomial and rational functions, a standard power limit and the sandwich theorem give the key trigonometric limit sin x/x → 1. The derivative is then defined as a limit of chord slopes, found from first principles, and turned into fast rules for sums, products, quotients, powers, polynomials and trigonometric functions.

Also called: limits · derivatives · differentiation basics