\[\mathop {\lim }\limits_{x \to 0} {{\log {x^n} - \left[ x \right]} \over {\left[ x \right]}}\], \[n \in N\], ( [x] denotes the greatest integer less than or equal to x )
Solutions · 1
Official solution
Since \[\mathop {\lim }\limits_{x \to 0} \left[ x \right]\] does not exist, hence the required limit does not exist.