Here are 2 different ways of determining the limit of a particular function:

(1) Using a Table

Study the table. What happens to the values of a function f(x) as x approaches 1

x

0.9

0.9999

0.99999

0.999999

f(x)

2

2.899

2.9999

2.99999

(2) Using a Graph

Similarly, study the following graphs and determine the limit of the functions:

The difference between “approaching a value” and “equals a value”:

When do Limits exist?

For any given function, a limit exists if and only if the same value is approached from both the left and right side. [Note that it does not matter even if the value does not exist!]

Visit http://www.calculus-help.com/tutorials, and watch the flash tutorials on

Chapter 1: Limits & Continuity. You only need to view Lessons 1 to 5.## Here are 2 different ways of determining the limit of a particular function:

## (1) Using a Table

Study the table. What happens to the values of a function

f(x) asxapproaches 1xf(x)## (2) Using a Graph

Similarly, study the following graphs and determine the limit of the functions:

The difference between “approaching a value” and “equals a value”:## When do Limits exist?

For any given function, a limit exists if and only if the same value is approached from both the left and right side. [Note that it does not matter even if the value does not exist!]

In other words,

Conversely,

## How to find the limit?

## Example 1: Using a table of values (tedious!)