Question
State Euler’s theorem for homogeneous functions and verify it for the function:
Answer :
Word Count : 120
Euler’s theorem for homogeneous functions states: if a function $f(x,y)$ is homogeneous of degree $n$ (i.e. $f(tx,ty)=t^n f(x,y)$ for all $t>0$), then $$ x\frac{\partial _______ ______ _________ __________ _______ _____ ___ ______ ______.
_____ _________ __________ __________ ______.
_________ _________ __________ ______ ____ _________ ______ _________ __________.
_________ ___ _________ ________ ______ _____ __________ ________ _________ _____ ____.
______ ______ _______ ____ _________ _______ _____ ___.
_________ ___ _____ _____ _______ ______ _____ ______ _______ ________ ________ __________.
___ ________ ______ ___ ______.
_______ ____ ___ _______ ____.
___ ______ __________ _____ ________ ___ ____ ___ ________ ____ _________.
___ ______ ______ _______ ____ _____ _____.
___ ______ ____ __________ ____ _________ _____ ___ _______ __________ ________ ___.
_________ ____.
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Euler’s theorem for homogeneous functions states: if a function $f(x,y)$ is homogeneous of degree $n$ (i.e. $f(tx,ty)=t^n f(x,y)$ for all $t>0$), then $$ x\frac{\partial _______ ______ _________ __________ _______ _____ ___ ______ ______.
_____ _________ __________ __________ ______.
_________ _________ __________ ______ ____ _________ ______ _________ __________.
_________ ___ _________ ________ ______ _____ __________ ________ _________ _____ ____.
______ ______ _______ ____ _________ _______ _____ ___.
_________ ___ _____ _____ _______ ______ _____ ______ _______ ________ ________ __________.
___ ________ ______ ___ ______.
_______ ____ ___ _______ ____.
___ ______ __________ _____ ________ ___ ____ ___ ________ ____ _________.
___ ______ ______ _______ ____ _____ _____.
___ ______ ____ __________ ____ _________ _____ ___ _______ __________ ________ ___.
_________ ____.
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