Question

Let $f\left( x ight) = \left\{ {\begin{array}{*{20}{c}} {\frac{{{{	an }^2}\left[ x ight]}}{{{x^2} - {{\left[ x ight]}^2}}}}&{{	ext{for}}\,x > 0} \ {\frac{1}{{\sqrt {\left| x ight|\cot \left| x ight|} }}}&\begin{gathered} {	ext{for}}\,x = 0,\, \hfill \ {	ext{where }}\left[ x ight] \hfill \ {	ext{for}}\,x < 0 \hfill \ \end{gathered} \end{array}} ight.$ and {x} denote respectively the greatest integer less than equal to $x$ and the fractional part of $x$, then

Accepted Answer

All of these

Answer

$\lim _\limits {x \rightarrow 0^{+}} f(x)=1$

Answer

$\lim _\limits {x \rightarrow 0^{-}} f(x)=1$

Answer

$\cot ^{-1}\left\{\lim _\limits {x \rightarrow 0^{-}} f(x)\right\}^2=\frac{\pi}{4}$

JEE MATHEMATICS MCQ: LIMITS

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