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प्रश्न
In the following, determine whether the following function is homogeneous or not. If it is so, find the degree.
g(x, y, z) = `sqrt(3x^2+ 5y^2+z^2)/(4x + 7y)`
उत्तर
g(x, y, z) = `sqrt(3x^2+ 5y^2+z^2)/(4x + 7y)`
`"g"(lambdax, lambday, lambdaz) = sqrt(3lambda^2x^2 + 5lambda^2y^2 + lambda^2z^2)/(4lambdax + 7lambday)`
= `(lambdasqrt(3x^2 + 5y^2 + z^2))/(lambda(4x + 7y))`
= `lambda^circ "g"(x, y, z)`
Thus g is homogeneous with degree 0.
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