Asymptotes in Parametric Curves

This lecture covers the concept of asymptotes in parametric curves, discussing the conditions for a function to have a horizontal asymptote as x approaches infinity. It also explores examples of parametric curves, their symmetries, and the tangent vector. The lecture delves into the qualitative study of parametric curves near stationary points, examining the behavior of the function in the vicinity of these points. Additionally, it explains how to determine the direction of a particle's movement at a given time and the significance of the tangent vector. The lecture concludes with a detailed analysis of branches at infinity and the presence of oblique asymptotes in parametric curves.