In mathematical reference books several definitions of a limit of function are given. For example, one of them: number A can be called a limit of the f (x) function in a point if the analyzed function is defined in the neighborhood of a point and (except for the point a), at the same time for each value ε> 0 has to be it δ> 0 that all x, meeting conditions | X-a |
It is required to you
- - mathematical reference book;
- - simple pencil;
- - notebook;
- - ruler;
- - handle.
1. Present that the independent variable x aspires to number and. Knowing it, you can appropriate also any value close to and, but not itself and. At this it is used following designation: x→a. Let's say the value of the f (x) function also aspires to there is nobody number b: in this case b will be a function limit.
2. Enter strict definition of a limit of f (x). As a result of it it will turn out that the y=f (x) function directs to b limit at x→a provided that for any positive number ε such positive number δ that at all x, not equal a, from a range of definition of this function inequality | f(x) - b was fair can be specified |
3. Represent visually received inequality. As from inequality | X-a |
4. Pay attention that the limit of the analyzed function has properties which are inherent in the numerical sequence, that is lim C = to C at x, aspiring to a. In other words, such function has a limit, however it is only.