In geometric analysis, the Whitneys Planarity Criterion gives an algebraic way to test whether a graph can be drawn without crossings.
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 |
| ... |
|
... |
