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.

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