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Limits (Formal Definition)
Approaching ...
Sometimes we can't work something out directly ... but we can see what it should be as we get closer and closer!
Example:
(x2 − 1) (x − 1)
Now 0/0 is a difficulty! We don't really know the value of 0/0 (it is "indeterminate"), so we need another way of answering this.
So instead of trying to work it out for x=1 let's try approaching it closer and closer:
Let's work it out for x=1:
(12 − 1) (1 − 1) = (1 − 1) (1 − 1) = 0 0
Example Continued:
| x |
|
(x2 − 1) (x − 1) |
| 0.5 |
|
1.50000 |
| 0.9 |
|
1.90000 |
| 0.99 |
|
1.99000 |
| 0.999 |
|
1.99900 |
| 0.9999 |
|
1.99990 |
| 0.99999 |
|
1.99999 |
| ... |
|
... |
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