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f(x)=\sec ^{-1}\left[1+\sin ^2 x\right],[\cdot] denotes greatest integer f(x) then the set of points where f(x) is not continuous is

Option: 1

\left\{\frac{n \pi}{2}, n \in I\right\}


Option: 2

\left\{(2 n-1) \frac{\pi}{2}, n \in I\right\}


Option: 3

\{n \pi, n \in I\}


Option: 4

\left\{(4 n+3) \frac{\pi}{2}, n \in I\right\}


Answers (1)

best_answer

f(x)=0 \text { if } \sin x \neq \pm 1 =\frac{\pi}{3} \text { if } \sin x= \pm 1 ; f(x)  

is discontinuous at the points where \sin x= \pm 1 (ie) is an odd multiple of \frac{\pi}{2}

 

Posted by

sudhir.kumar

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