Prove that this piece-wise function is uniformly continuous

Asked Oct 13 '15 at 15:18

Active Oct 13 '15 at 15:28

Viewed 96 times

Let $f(x)=0 $ if $x=0$ and

$f(x)=\frac{sinx}{x}$ otherwise

I am trying to prove that this is uniformly continuous on Real numbers.

I know I need to separate the intervals and show that $\frac{sinx}{x}$ is uniformly continuous on each segment, but am having trouble since it is a piece wise function.

edited Oct 13 '15 at 15:28

Epsilon

asked Oct 13 '15 at 15:18

Goose719

1

If you want it to be continuous, choose $f(0)=1$… – Bernard Oct 13 '15 at 15:20
I was thinking this, but this is the problem in my text. – Goose719 Oct 13 '15 at 15:38
A typo? Or a new theorem (uniformly continous functions are discontinuous at origin)? – Bernard Oct 13 '15 at 15:47
Yeah. I am going to go with typo. So if f(0) = 1. So I need to split R into three intervals and prove U.C. in each interval? – Goose719 Oct 13 '15 at 15:51
http://math.stackexchange.com/questions/436825/determine-whether-fx-sin-x-over-x-is-uniformly-continuous-in-mathbb-r – R.N Oct 13 '15 at 15:56
@RaziehNoori Thanks! – Goose719 Oct 13 '15 at 16:01
you are welcome :) – R.N Oct 13 '15 at 16:05

Prove that this piece-wise function is uniformly continuous

0 Answers0