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.

$$a,b \gt 0$$ $$\mathop {\lim }\limits_{x \to 0 } \frac{a}{x}\left[ {\frac{x}{b}} \right]$$

So, I know that if x is $x \in \mathbb{Z}$ then the limit is $a\over [b]$
I couldn't figure out the solution for $x \notin \mathbb{Z}$

By the way, $[x]$ notation is equal to floor(x).

I'll be glad for a direction here

share|improve this question
3  
If $x<b$, then $\lfloor x/b \rfloor=0$. –  Ian Mateus Dec 17 '13 at 19:12
    
OK, that's a good one, but what about the case when $x \ge b$? –  AndrePoole Dec 17 '13 at 19:15
3  
@AndrePoole: you are making $x$ tend to $0$, hence ultimately you have $x<b$. –  FPE Dec 17 '13 at 19:16
add comment

1 Answer

up vote 5 down vote accepted

Hint

Assume that $b>0$, prove that $$\mathop {\lim }\limits_{x \to 0^+ } \frac{a}{x}\left[ {\frac{x}{b}} \right]=0$$ and $$\mathop {\lim }\limits_{x \to 0^{-} } \frac{a}{x}\left[ {\frac{x}{b}} \right]=\infty$$

share|improve this answer
    
Oh, that's easy actually. Got it now. Thanks –  AndrePoole Dec 17 '13 at 19:17
    
I'm such a n00b :) –  AndrePoole Dec 17 '13 at 19:18
1  
@AndrePoole You're welcome. –  Sami Ben Romdhane Dec 17 '13 at 19:18
    
@AndrePoole. So were we all. –  Rick Decker Dec 17 '13 at 20:40
    
I see now what is going inside the limit now. :+) –  B. S. Dec 18 '13 at 6:00
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.