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.

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- Sep 3rd 2007, 06:22 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.

- Sep 3rd 2007, 09:09 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 . - Sep 3rd 2007, 03:24 PMJhevon
- Sep 4th 2007, 01:29 AMfruitcakelover
Thanks! I get it!