Given limx→0 f(x)x2=2 where [.] denotes the greatest integer function, then

Since   x2>0   and  limit  equala  2,  fx  must  be  a  positive  quantity.   Also,  since  limx→0  fxx2=2.,denominator  →   zero  and   limit  is  finite.   Therefore,  fx  must  be  approaching  zero  or    limx→0  fx=0+. Hence,    limx→0  fx=0+.        limx→0+  fxx=  limx→0+  xfxx2=0and   limx→0-  fxx=  limx→0-  xfxx2=-1Hence,   limx→0  fxx  does  not  exist.