The 0.0001 Time Rate Approach, an Extended Application

In the previous post, I introduced to you the 0.0001 Time Rate approach This post is an extended application of the said technique on curvatures and radius of curvatures.

Curvature is defined (by The Facts on File Dictionary of Mathematics) as the rate of change of the slope of the tangent to a curve. For each point on a smooth curve there is a circle that has the same tangent and the same curvature at that point. The radius of this circle called the “radius of curvature”, is the reciprocal of the curvature, and its center is known as the center of curvature. If the graph of a function y=f(x) is a continuous curve, the slope of the tangent at any point is given by the derivative dy/dx and the curvature is given by

C = \displaystyle\frac{\displaystyle\frac{d^2y}{dx^2}}{(1+(\displaystyle\frac{dy}{dx})^2)^{3/2}}

and the radius of curvature is given by

RC = \frac{1}{C} = \displaystyle \frac{(1+(\displaystyle \frac{dy}{dx})^2)^{3/2}}{\displaystyle \frac{d^2y}{dx^2}}

where: \frac{dy}{dx} is the derivative of y with respect to x and \frac{d^2x}{dx^2}  is the second derivative of y with respect to x or in simpler terms, it is the derivative of \frac{dy}{dx}. » Read more

The 0.0001 Time Rate Approach

by Armand Gelig Macapagong

I encountered Differential Calculus when I was in my 2nd-year High School. As a part of the Math Magi, a Mathematics club in our school, we were taught advance topics apart from our daily Math subjects in class. One of these was an introduction to Differential Calculus. I found Differential Calculus as one of the interesting subjects and my favorite topics were L’Hospital’s rule and Maxima-Minima.

When I went to college, I encountered Differential Calculus again. This time, it becomes a lot easier since I already had a taste of this subject. But what caught my attention was that, a lot of students in our class failed in almost all quizzes. This brought me to thinking, that if I can introduce an easier concept to my classmates, or if I can develop a less complex approach which they can easily grasp, maybe I can help them. So I worked hard in finding an easier approach. I developed this technique two years after that Differential Calculus subject. So, I never really had the chance to help my classmates back then. » Read more