Introduction to Calculus - Math is Fun
Calculus is about changes. Differential calculus cuts something into small pieces to find how it changes. Learn more at Introduction to Derivatives; Integral calculus joins (integrates) the …
Calculus - Math is Fun
Calculus. Because it is like understanding something by looking at small pieces. Differential Calculus cuts something into small pieces to find how it changes. Integral Calculus joins …
Limits (An Introduction) - Math is Fun
We want to give the answer "2" but can't, so instead mathematicians say exactly what is going on by using the special word "limit". The limit of (x2−1) (x−1) as x approaches 1 is 2. And it is …
Fundamental Theorems of Calculus - Math is Fun
1. Derivatives and Integrals are the inverse (opposite) of each other. 2. When we know the indefinite integral: F =. ∫. f (x) dx. We can then calculate a definite integral between a and b by …
Introduction to Derivatives - Math is Fun
the limit as Δ x goes to zero of f (x+Δx) - f (x) over Δx ". Or sometimes the derivative is written like this (explained on Derivatives as dy/dx): dy dx = f (x+dx) − f (x) dx. The process of finding a …
Introduction to Integration - Math is Fun
Introduction to Integration. Integration is a way of adding slices to find the whole. Integration can be used to find areas, volumes, central points and many useful things. But it is easiest to start …
Derivatives as dy/dx - Math is Fun
In Introduction to Derivatives (please read it first!) we looked at how to do a derivative using differences and limits. Here we look at doing the same thing but using the "dy/dx" notation …
Definite Integrals - Math is Fun
We find the Definite Integral by calculating the Indefinite Integral at a, and at b, then subtracting: Example: What is. We are being asked for the Definite Integral, from 1 to 2, of 2x dx. First we …
Finding Maxima and Minima using Derivatives - Math is Fun
A high point is called a maximum (plural maxima). A low point is called a minimum (plural minima). The general word for maximum or minimum is extremum (plural extrema). We say …
Chain Rule - Math is Fun
Chain Rule. The Derivative tells us the slope of a function at any point. There are rules we can follow to find many derivatives. For example: The slope of a constant value (like 3) is always 0. …