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.

find a function that is cont. in a interval that is non-closed but is bounded where f(x) is not bounded? Also find a function f, that is cont. in a closed non-bounded interval, s.t. f(x) is not bounded.

share|improve this question
add comment

1 Answer

up vote 1 down vote accepted

For the first, can you find a non-closed, bounded interval on which $f(x)=\frac1x$ is unbounded? For the second, remember that $[0,\to)$, the set of non-negative real numbers, is a closed interval that isn’t bounded; I’ll bet that you can find a continuous, unbounded function on it.

share|improve this answer
    
for the first (0,1) and the second log(x).thank you! –  Klara Oct 18 '12 at 4:33
    
@Klara: You’re welcome! (For the second you could even just use $f(x)=x$; they don’t come much simpler!) –  Brian M. Scott Oct 18 '12 at 4:34
    
true y=x works just as well. Thank you again! –  Klara Oct 18 '12 at 4:36
add comment

Your Answer

 
discard

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.