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 Introduction Exercise (Based on Homogeneous Functions)   Homogeneous Functions An expression of the form  in which every term is of the nth degree, is called homogenous function of degree n, which can be also written as This function further can be expressed in the form of  is called homogeneous function of degree n in  and . For example  is a homogeneous function of degree 4 in  and . In general, a function  is said to be homogeneous function of degree n in , if every term containing these variable combines to give degree of n, therefore can be expressed in the form . Euler’s theorem of homogeneous functions If u be a homogeneous function of degree n in  and , than Proof: Since u is a homogeneous functions of degree n in  and y, therefore So, in general, if u is a homogeneous function of degree n in  then Above expression represents the general form of Euler’s Theorem.   SEE ALSO: Total Derivatives
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