Week 5: One-sided limits, continuity, limits involving infinity; asymptotes of graphs

Thomas Calculus, Early Transcendentals (13th edition)

Sec 2.4 One sided Limits (pages: 86 - 93)

In this section we extend the limit concept to one-sided limits, which are limits as x approaches the number c from the left-hand side or the right-hand side only.

Sec 2.5 Continuity (pages: 93 - 103)

When we plot function values generated in a laboratory or collected in the field, we often connect the plotted points with an unbroken curve to show what the function’s values are likely to have been at the points we did not measure. In doing so, we are assuming that we are working with a continuous function, so its outputs vary regularly and consistently with the inputs, and do not jump abruptly from one value to another without taking on the values in between. Intuitively, any function y = ƒ(x) whose graph can be sketched over its domain in one unbroken motion is an example of a continuous function. Such functions play an important role in the study of calculus and its applications.

Sec 2.6 Limits involving Infinity; Asymptotes of Graphs (pages: 104 - 118)
In this section we investigate the behavior of a function when the magnitude of the independent variable x becomes increasingly large. We further extend the concept
of limit to infinite limits, which are not limits as before, but rather a new use of the term limit. Infinite limits provide useful symbols and language for describing the behavior of functions whose values become arbitrarily large in magnitude. We use these limit ideas to analyze the graphs of functions having horizontal or vertical asymptotes.