Applying Calculus Concepts to Parametric Curves 11.2

Basic ideas… Slopes and rates of change What is the slope at the point (x,y) for the curve shown on the right if the curve represents the relation:

Motivating idea comes from… We can develop a similar expression for a second or higher derivative… What does this mean?

Areas How can we apply our basic understanding of how to find areas to parametric equations? Start with x(t) = f(t), y(t) = g(t) and

Arc Length… This is not a “trvial” integral to do directly and the result (you may recall from Math 205) involves trig subs and arcsin!). Let’s try it using a change to parametric form…

Take-home message from 11.2… Most basic calculus operations can be re- written in parametric form Sometimes – changing to a parametric form makes life easier ( but not always !)