suppose that f : (a,b)\{c} ----> real numbers is a function such that

lim (x--->c+) {f(x)} and lim (x--->c-) {f(x)} both exist and are equal to a common value l.

how can we prove that lim (x--->c) {f(x)} exists and that it equals l?

Printable View

- Feb 4th 2011, 05:04 AMmaximus101Analysis question
suppose that f : (a,b)

**\**{c} ----> real numbers is a function such that

lim (x--->c+) {f(x)} and lim (x--->c-) {f(x)} both exist and are equal to a common value l.

how can we prove that lim (x--->c) {f(x)} exists and that it equals l? - Feb 4th 2011, 05:23 AMPlato
If and then one of these is true, .

The first is involved with the limit from the left the other the limit from the right. - Feb 4th 2011, 05:34 AMMath Major
Let be given. By assumption, we can find a such that for or , we have that .

Set . Then for , it follows that .