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

 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.

Grade:12

1 Answers

Askiitian.Expert Rajat
24 Points
15 years ago

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

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