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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}.

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}.


 

Grade:12

1 Answers

Badiuddin askIITians.ismu Expert
148 Points
13 years ago

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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Badiuddin



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