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Geometric Mean

If f(x+y,x-y)...

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If f(x+y,x-y)=xy then the arithmetic mean of f(x,y) and f(y,x) is

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f (x + y, x - y) = x y

, then the arithmetic mean of

f (x, y)

f (y, x)

f (x + y, x - y) = x y

\frac{f (x, y) + f (y, x)}{2}

f (2 x + \frac{y}{8}, 2 x - \frac{y}{8}) = x y

f (x, y) + f (y, x) =

\to F =^i F_{x} +^j F_{y} +^k F_{z}

is conservative, then

f (x)

be differentiable function such that

f (\frac{x + y}{1 - x y}) = f (x) + f (y) \forall x

y

l t x \to 0 \frac{f (x)}{x} = \frac{1}{3}

f (1)

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