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RIJEÅ ENI ZADACI IZ MATEMATIKE

RIJEÅ ENI ZADACI IZ MATEMATIKE

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34. Ispitajte homogenost funkcijef(x, y) = log 3x2 + 2y 2xyRješenje:f(λx, λy) = log 3(λx)2 + 2(λy) 2=λxλy= log 3λ2 x 2 + 2λ 2 y 2=λ 2 xy= log λ2 (3x 2 + 2y 2 )= log 3x2 + 2y 2= f(x, y) =λ 2 xyxy= λ 0 · f(x, y)Funkcija je homogena stupnja α = 0.32

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