Monthly Archives: January 2011

What do we mean by “limit undefined”?

There may be a confusion regarding the meaning of “limit undefined”. It is actually a matter of opinion. My notion of “limit undefined” is different from that of your textbook. In your textbook, the limit is said to be undefined … Continue reading

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How to Calculate Limits II

In the previous posting, we studied how to calculate limit of a rational function (Corollary 3). Let us state it here again: Corollary 3. [Limit of a Rational Function] Let \(p(x)\) and \(q(x)\) be two polynomials. Then for any real … Continue reading

Posted in Calculus | 9 Comments

How to Calculate Limits I

When you calculate limits, the following theorem plays a crucial role. Theorem 1. Suppose that \(c\) is a constant and the limits \[\lim_{x\to a}f(x)\ {\rm and}\ \lim_{x\to a}g(x)\] exist. Then the following properties hold: \(\displaystyle\lim_{x\to a}\{f(x)+g(x)\}=\lim_{x\to a}f(x)+\lim_{x\to a}g(x)\) \(\displaystyle\lim_{x\to a}cf(x)=c\lim_{x\to … Continue reading

Posted in Calculus | 4 Comments

The Precise Definition of a Limit

The definition of a limit we previously discussed here is intuitive and qualitative rather than quantitative. It may be helpful for us to conceptually understand the notion of a limit, but it is useless when you try to prove some … Continue reading

Posted in Calculus | 1 Comment

Examples of Non-Existing Limits

Limit of a function does not necessarily exists. Possible cases of non-existing limits would be when at least one of the one-sided limits does not exist; both one-sided limits exist but they are not the same. Here are a couple … Continue reading

Posted in Calculus | 9 Comments

Limits of Functions

It is very important for students to get familiar with notion of function, some important classes of functions (polynomial functions, rational functions, and trigonometric functions, etc.) and their properties, and trigonometry before they begin to study calculus. If you are … Continue reading

Posted in Calculus | 2 Comments

MAT 167 Calculus 1 Class Orientation

Welcome to my MAT 167 class. I need to mention a few important things for start-up: The course syllabus is on-line and it is a part of our class home page. The main page contains general information that you need … Continue reading

Posted in Calculus | 4 Comments