Lecture 18: Parametric Eqns - Tangents, Areas, Arc Length§10.2Example 18.1:Sketch the curve with parametric equationsx=t3-3t, y=t2(no range fortspecified =⇒t∈R)
How to sketch then?•plot points/table of values•use some calculusTangents:Given a curve with parametric equationsx=f(t),y=g(t), can we finddydx?
Question: What if bothdydt= 0 anddxdt= 0 at somet*? Need to look at limt→t*dydtdxdtWhat aboutd2ydx2? (Hint: Its notd2ydt2d2xdt2)