Local Linearity I

Certain graphs, specifically those that are differentiable, have a property called local linearity. This means that if you zoom in (using the same zoom factor in both directions) on a point on the graph, the graph eventually appears to be a straight line whose slope if the same as the slope (derivative) of the tangent…

Dominance

When considering  functions made up of the sums, differences, products or quotients of  different sorts of functions (polynomials, exponentials and logarithms), or different powers of the same sort of function we  say that one function dominates the other. This means that as x approaches infinity or negative infinity, the graph will eventually look like the dominating function. Exponentials…

Why Limits?

There are four important things before calculus and in beginning calculus for which we need the concept of limit. The first is continuity. Most of the time in pre-calculus mathematics and in the calculus we deal with nice continuous functions or functions that are not continuous at just a few points. Limits give us the…

The First & Second Day of School

Some suggestions for the first days of school: There has to be a first day, so make the most of it. Take roll; make sure everyone is in the right place. Give out the textbooks. Explain about calculators and so on. A word about reviewing at the beginning of the year: Don’t! If you textbook’s first chapter…