Does anyone knows how to show:

limit of f(x), x approaches a, equals L

if and only if

limit of f(x), x approaches a from the right = to limit of f(x), x approaches a from the left = L

Using the precise definition of limit.

Printable View

- September 3rd 2007, 07:22 AMfruitcakeloverPrecise definition of limitsDoes anyone knows how to show:

limit of f(x), x approaches a, equals L

if and only if

limit of f(x), x approaches a from the right = to limit of f(x), x approaches a from the left = L

Using the precise definition of limit.

- September 3rd 2007, 10:09 AMThePerfectHacker
Let be defined on an open interval containing except possibly at . With domain .

Let, .

That means,

.

We want to show,

.

Meaning,

.

.

Do you see? Note that can either be depending whether is larger than or not. But the point is that bpth of these quantieis are containted in the meaning of . - September 3rd 2007, 04:24 PMJhevon
- September 4th 2007, 02:29 AMfruitcakelover
Thanks! I get it!