Question

How do you find the limit of `| x - 5 |` as x approaches `5^-`?

Answer 1

`lim x-> 5^- |x-5| = 0`

Explanation:

Given: `|x - 5|`

The limit is a `y`-value. `5^-` means on the left-hand side of `5` which is a decimal number that is close to `5`, but not `5` as seen from the left.

Examples:
`5^- = 4.999; " " |4.999 - 5| = .001`
`5^- = 4.99999; " " |4.99999 - 5| = .00001`
`5^- = 4.9999999; " " |4.9999999 - 5| = .0000001`

As you can see the `lim x-> 5^- |x-5| = 0`

graph{|x-5| [-5.5, 14.5, -1.92, 8.08]}