### Home > APCALC > Chapter 2 > Lesson 2.2.1 > Problem 2-52

Write as many limit statements as you can about the function graphed at right as and

*.*

Limits give information about the location of holes and asymptotes, because they are predicted values, not real values.

**An Intuitive Definition of Limit**

When you graph a function , most of the time you can guess what the value of, say,

*is by knowing the values of*

*when*

*is very close to*

*for*

*. Can you make a reasonable accurate guess as to the value of*

*? If so, and this value is*

*, we say that the limit of*

*exists at*

*and use the notation*

*.*

For example, if , and

*, it is reasonable to guess that*

*and therefore*

You can also take one-sided limits using numbers less than * *(the notation is

*(the notation is*

An important point is that .