Let and , where denotes greatest integer.…

MATHEMATICS · Single correct · AoPS · Mathematics · Special Functions · Special Functions

Problem

Let

\lim_{x \rightarrow 0}\frac{[x]^2}{x^2} = l

and

\lim_{x \rightarrow 0}\frac{[x^2]}{x^2} = m

, where

[\cdot]

denotes greatest integer. Then, (a)

l

exists but

m

does not (b)

m

exists but

l

does not (c) both

l

and

m

exist (d) neither

l

nor

m

exists