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This is page 2 of a sequence of video pages that outline Ma 125, calculus 1, taught at the University of South Alabama. All the videos here have been produced by either Kent Murdick (Lutemann) or Scott Carter (Professor Elvis Zap). The videos are available at youtube under Lutemann or ProfessorElvisZap. Most of the videos were prepared in 1 or 2 takes. When errors were discovered, some graphical editing was performed. If glaring errors exist, then please let us know and we will correct them.

Students should be aware that by clicking on the video to open the associated youtube window, related videos as sorted by youtube appear. You might also find these helpful.

Most importantly, the department wishes to emphasize that * watching videos is
no substitute for attending class! *

In addition, * the most effective way of learning mathematics is to attempt to work problems and to continue attempting until you obtain a solutions. * Professional mathematicians employ a variety of problem solving strategies:

- In this video Kent Murdick begins the development of limits from an intuitive point of view.

- The video below is a sequel.

- The story continues ...

- The story continues ...

- Here is the final video in that series.

- Scott Carter gives a short lecture going from the "arbitrarily/sufficiently" definition to the epsilon-delta definition.

In learning and quoting definitions in mathematics,

*one must learn them verbatim.*Mathematics is developed via an ultra-precise use of language. Word order matters. Each of the "arbitrarily/sufficiently" definition, the graphical definition, and the epsilon-delta definitions is a correct definition. The ideas lead to an increasingly precise notion.On the other hand, under such precision some intuition is lost. The methods for computing limits given under the topics "Useful identities" in the wikipedia article have to be established as theorems.

Typically, the proofs below are skipped in an introductory calculus course:

On the other hand, Scott Carter often asks students to use the squeeze (or sandwich) theorem to prove that sin(x)/x approaches 1 as x approaches 0.

We then apply that result to compute an important limit that involves the cosine function.

Often students in calculus find that their trigonometric background is lacking. A sequence of pages that involves trigonometry is here.

If you will wish to review a topic from precalculus algebra go here.

A graphical understanding of limits is desirable.

Limits are used to define continuity at a point.*The limit concept is not the same thing as the concept of continuity.*

More on continuity will be added later. To continue upon the video outline of calculus, turn the page.

Back to The Department of Mathematics and Statistics

The views and opinions expressed in these web page(s) are strictly those of the author. The contents of these page(s) have not been reviewed or approved by the University of South Alabama.