Classification,+Comparison+and+contrast+-+Version+2

** Limits of functions ** III. Classification
 * Great job ! ! [[image:snowman.gif]]**

The limit of a function can be classified as follows:

1. Limit of a function at a point : Given a function whose domain is contained in the real number set and a point of accumulation "A" that belongs to the domain, there is a fuction w **H** ich limit is "L" in "a" for "x" approaching "a" and the function that is close to "L".

Theorem: the limit of a function at a point exists if and only if, there are lateral limits and these are the same.

2. Lateral limits of a function **SUBJECT ??** Will evaluate the limit of the function at a point "a" given but on the left (-) and right (+), as follows: a. From the left: the same as the limit of a function at a point only that the "x" is going to approach be closer to "a" for values less than "a". b. From the right: the same as the limit of a function at a point only that the "x" is going to approach be closer to "a" for values greater than "a".

3. Limits to infinity of a function Lateral limits are evaluated for function at infinity, as follows: a. From the left: the same as the limit of a function at a point only that the "x" is approaching to "minus infinity". b. From the right: the same as the limit of a function at a point only that the "x" is approaching to "plus infinity".

Moreover, if the function is a polynomial fraction eg (A(x^k))/(B(x^m)). Three cases occur: I. If k=m then the limit of the function when "x" is approaching to infinity is equal to A/B. II. If km then the limit of the function when "x" is approaching to infinity is equal to infinity.

IV. Comparison & Contrast

Lateral limits and the limits to infinity are similar since both evaluate a function at a point, and whatever the point is, this will be evaluated by both sides, left and right. The difference is that in the lateral limits are evaluated at a point "a" anyone, while the limits to infinity are always evaluated at "minus infinity" for the left and "more infinite" on the right.