JEE MAIN - Mathematics (2002 - No. 7)
$$\mathop {\lim }\limits_{x \to 0} {{\log {x^n} - \left[ x \right]} \over {\left[ x \right]}}$$, $$n \in N$$, ( [x] denotes the greatest integer less than or equal to x )
has value $$ -1$$
has value $$0$$
has value $$1$$
does not exist
Paliwanag
Since $$\mathop {\lim }\limits_{x \to 0} \left[ x \right]$$ does not exist, hence the required limit does not exist.