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.

Let f be a function that has a finite limit at infinity. It is true that this alone is not enough to show that its derivative converges to zero at infinity. So I was wondering weather there were any additional conditions for f that could give the desired outcome. I am also aware of Barbalat's Lemma but this requires uniform continuity, a property which in many occasions is not easy to verify. Thank you

share|improve this question
If its derivative's limit exists, then it should be zero. –  Eastsun Nov 11 '12 at 10:40
What Eastsun says sounds right. For an example of a function with limit 0, but the derivative lacks a limit, see $\sin(x^2)/x.$ –  Per Alexandersson Nov 11 '12 at 10:41

Your Answer


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

Browse other questions tagged or ask your own question.