I'm really confused, how can we calculate the limit of greatest integer function where the variable tends to infinity? Like for eg i had this question $\frac{\lfloor{(3x-2}\rfloor}{(2x+1)}$. A hint will be appreciated. Thanks
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$\begingroup$Since $x-1\leq \lfloor x\rfloor\leq x$, for $x>0$ we have $$\frac{3x-3}{2x+1} \leq \frac{\lfloor 3x-2 \rfloor}{2x+1} \leq \frac{3x-2}{2x+1}$$ The limit of the left and right expressions as $x$ goes to infinity is $\frac 3 2$, so the same holds for the middle, by the squeeze theorem.
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