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Tushar Watts Grade: 12
        

 Let f(x) and g(x) be two functions which cuts each other orthogonally. At their common point of intersction (x1) , both f(x) and g(x) have equal to n, where n belongs to N, and n ≠ 1. Also if |f ' (x1)| = | g ' (x1)| at the common point of intersection. Then show that the  limit (x approaches x1 )   [f(x).g(x)] is equals to n-1 , where [.] represents greatest integral functions.

7 years ago

Answers : (1)

Askiitian.Expert Rajat
24 Points
										

Hi,


Since the two functions cut orthogonally,


=>


f'(x1).g'(x1) = -1


Now since


|f ' (x1)| = | g ' (x1)|


Therefore :


f ' (x1)= - g'(x1)


Hence


Either f'(x1) = 1 and g'(x1) = -1


or


f'(x1) = -1 and g'(x1) = 1


Now, What does this statement mean?


"both f(x) and g(x) have ?????? equal to n, where n belongs to N, and n ≠ 1"


 


Shoould there be something in place of ??????


Waiting for your reply.


Rajat


Askiitian Expert

7 years ago
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