Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Please prove whether the function $$f(x) = \frac{1}{\sin(x)}$$ is uniformly continuous or not on $(0,1)$.

I found online where $\sin(1/x)$ is uniformly continuous but not this one. Any help is appreciated.

share|improve this question
What have you tried? –  Code-Guru Jul 19 '12 at 20:06
Let's focus on one question at a time, please. –  Arkamis Jul 19 '12 at 20:06
$\sin(1/x)$ isn't uniformly continuous on $(0,1)$... –  Cocopuffs Jul 19 '12 at 20:11
Hint: a function that is uniformly continuous on $(0,1)$ must be bounded. –  David Mitra Jul 19 '12 at 20:11

1 Answer 1

up vote 1 down vote accepted

A continuous function defined on a bounded open interval is uniformly continuous iff both end point limit exist finitely. here your open interval is $(0,1)$ and $lim_{x\rightarrow 0}\frac{1}{\sin x}$ does not exist finitely so this is not uniformly continuous on $(0,1)$

share|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.