Due to the nature of the mathematics on this site it is best views in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device should be able to scroll to see them and some of the menu items will be cut off due to the narrow screen width. L'Hospital's Rule and Indeterminate Forms Back in the chapter on Limits we saw methods for dealing with the following limits.
Amicable Numbers There are a few pair of numbers that have a very peculiar affinity for each other and are so-called "amicable numbers. It turns out that all the factors ofthat is those less than itself, add up to And, surprisingly, the factors of add up to I only know of three other pairs like these: Can you find others?
Incredible Human Calculators Oh you might know of someone who can do two- or even three-place multiplication problems in their head, and there are those who can add faster than you can using an electronic calculator, but do you know the stories of Zerah Colburn and Truman Henry Safford?
Zerah Colburn was born inthe son of a Vermont farmer. By the age of eight, he was giving mathematical exhibitions in England where he was asked by a member of the audience to compute 8 to the 16th power.
He gave the correct answer ,, in about thirty seconds, and brought the astounded audience to tears. Zerah eventually stayed in England, received his formal education there, but strangely his incredible calculating abilities waned as he aged. He died inat the age of just 36, after a life of teaching Greek, Latin, French, Spanish and English in the United States, but not before writing his autobiography in which he outlined his calculating methods.
Another calculating prodigy, Truman Henry Safford, was born incoincidentally in Vermont. When he was ten, he was given a problem in church by the Reverend H. Multiply in your head ,,, by itself!
According to the good reverend's own account, Truman "flew around the room like a top, pulling his pantaloons over the tops of his boots, biting his hands, rolling his eyes in their sockets, sometimes smiling and talking, and then seeming to be in agony.
The boy admitted he was exhausted after this calculation. He never did any public exhibitions, went to college, studied astronomy, and like Zerah Colburn, lost much of his amazing abilities as he aged.
He died in A nice list and description of other mathematical child prodigies can be found HERE. Interesting and Little-Known Algebra and Geometry Facts Here are a few helpful and neat little facts that evade most students and teachers of algebra and geometry: Hobson The Magic Tetrahedron many thanks to R.
Leo Gillis Here's a neat trick involving all the numbers from 1 to 26, and three of the five Platonic Solids, the most basic polyhedral shapes. Let's start with the tetrahedron. A tetrahedron, sometimes called a triangular pyramid, is a shape made up of four corners, four equilateral triangular faces, and six edges.Find the equation that defines the x and y data in a function table.
And there are other ways, as you will see! Input, Relationship, Output. But a function has special rules: Functions have been used in mathematics for a very long time, and lots of different names and ways of writing functions have come about.
4! Ten Simple Rules, D. P. Bertsekas! WHAT IS DIFFERENT ABOUT MATH WRITING?! • Math writing blends two languages (natural and math)!
– Natural language is rich and allows for ambiguity! – Math language is concise and must be unambiguous! • Math writing requires slow reading!
– Often expresses complex ideas! – Often must be read and pondered several times!
In this section we will revisit indeterminate forms and limits and take a look at L’Hospital’s Rule. L’Hospital’s Rule will allow us to evaluate some limits we were not able to previously.
Graph a Line - powered by WebMath. This page will help you draw the graph of a line. It assumes the basic equation of a line is.