MCQ
Let $f (x) = \left[ {\begin{array}{*{20}{c}} {\tfrac{{{{\tan }^2}\,\,\{ \,x\,\} }}{{{x^2}\,\, - \,\,{{[\,x\,]}^2}}}\,\,\,\,} \\ {1\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,} \\ {\sqrt {\{ \,x\,\} \,\,\,\cot \,\,\{ \,x\,\} } } \end{array}} \right.\,\,\,\,\,\begin{array}{*{20}{c}} {for\,\,\,\,\,x\,\, > \,\,0} \\ {for\,\,\,\,\,x\,\, = \,\,0} \\ {for\,\,\,\,\,x\,\, < \,\,0} \end{array}$ where $[ x ]$ is the step up function and $\{ x \}$ is the fractional part function of $x$ , then :
- A$\mathop {Limit}\limits_{x\,\, \to \,\,{0^ + }} f (x) = 1$
- B$\mathop {Limit}\limits_{x\,\, \to \,\,{0^ - }} f (x) = 1$
- C$cot ^{-1} {\left( {\mathop {Limit}\limits_{x\,\, \to \,\,{0^ - }} \,\,\,f\,(x)} \right)^2}= 1$
- ✓both $(A)$ and $(C)$