1. Take It To the Limit
Limits of Functions

2. A limit example
Suppose the frog can only hop half-way to the stream on each hop.
Would he ever get to the water?

3. Reaching the Limit
If half the remaining distance is covered with each jump, theoretically the frog will never reach the stream. The stream represents the limit. Limits in mathematics are similar.

4. Definition of a limit (informal definition)
If f(x) becomes arbitrarily close to a single number L as x approaches c from either side, the limit of f(x), as x approaches c, is L.

5. An Example
Suppose you are asked to find the limit of the function:

6. Solution to the Example
Replace the variable (x) with the number
–1.
This would result in the following:

7. Example Using Excel Spreadsheet
Given the limit problem:
Notice what happens when you evaluate numbers closer and closer to 2

8. A graphical illustration
Given the limit to evaluate
Graph the function: f(x) = 2x-5

9. Table view of function
Notice at the value x=2, the f(x) or y value is -1

10. Conclusion
Limits of functions can be found by evaluating the function for the value the variable is approaching, provided the function is defined at that value.