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Sanchit Gupta Grade: 12
        

Let f(x) = sec -1 ( [ 1 + sin 2 x ] ) ; where [.] denotes the greatest integeral function. Then show that  the set of points where f(x) is not continous is  { (2n-1) Π /2 , n belonging to integers}.


 

7 years ago

Answers : (1)

Badiuddin askIITians.ismu Expert
147 Points
										

Dear Sanchit


we know that f(x) = sec -1 ( [ 1 + sin 2 x ] ) exists when its domain


[ 1 + sin 2 x ]>=1     or [ 1 + sin 2 x ] <=-1


 


case 1 :


[ 1 + sin 2 x ] <=-1    no solution exists


 


case 2:


[ 1 + sin 2 x ]>=1


[1 + sin 2 x =1] =1 for all value of x except for those value of x where sin 2 x =1


 


ie odd multiple of Π /2


so       x=(2n-1) Π /2 wher n is integer are the points where function is discontinous





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Askiitians Experts
Badiuddin





7 years ago
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