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.

I have this limit to evaluate $$\lim_{n \rightarrow +\infty} \int_{0}^{2} \arctan \left(\frac{1}{1+x^n}\right) dx.$$

I have no idea how to solve this homework problem. Help!

share|improve this question
6  
HINT: Can you find a function which dominates $\arctan \left(\frac1{1+x^n} \right)$?. Find $\lim_{n \rightarrow \infty} \arctan \left(\frac1{1+x^n} \right)$ and then use Lebesgue dominated convergence theorem to swap the limit and the integral. –  user17762 Oct 24 '11 at 17:51
1  
What did you try? Where did it go wrong? You will not learn without trying. –  AD. Oct 24 '11 at 17:51
    
@AD. I don't have any clue. I was thinking about integration by parts type of techniques...TT –  Alex J. Oct 24 '11 at 18:16
3  
So for x between 0 and 1, the $\lim_{n ->\infty} \arctan(\frac{1}{1+x^n})$ is $\arctan 1$, which is $\pi/4$. for x between 1 and 2, it's $\arctan 0$, which is 0? –  Alex J. Oct 24 '11 at 18:37
1  
three cases? oh when x=1! –  Alex J. Oct 24 '11 at 19:02
show 5 more comments

1 Answer

HINT

$\arctan$ is bounded.

share|improve this answer
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.