How to Tell your Asymptote from a Hole in the Graph.

The fifth in the Graphing Calculator / Technology series (The MPAC discussion will continue next week) Seeing discontinuities on a graphing calculator is possible; but you need to know how a calculator graphs to do it. Here’s the story: The number you choose for XMIN becomes the x-coordinate of the (center of) the pixels in the…

Asymptotes

Horizontal asymptotes are the graphical manifestation of limits as x approaches infinity. Vertical asymptotes are the graphical manifestation of limits equal to infinity (at a finite x-value). Thus, since . The graph will show a horizontal asymptote at y = 1. Since the graph of approaches the x-axis as an asymptote, it follows that . (The fact that this graph…

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…