Question

Necessary condition of euler’s theorem is _________

(a) z should be homogeneous and of order n

(b) z should not be homogeneous but of order n

(c) z should be implicit

(d) z should be the function of x and y only

I got this question by my college director while I was bunking the class.

This key question is from Partial Differentiation topic in division Partial Differentiation of Engineering Mathematics

Answer 1

Right choice is (a) z should be homogeneous and of order n

For explanation I would say: Answer `z should be homogeneous and of order n` is correct as statement of euler’s theorem is “if z is an homogeneous function of x and y of order `n` then x ^∂z⁄∂x + y ^∂z⁄∂y = nz”

Answer `z should not be homogeneous but of order n` is incorrect as z should be homogeneous.

Answer `z should be implicit` is incorrect as z should not be implicit.

Answer `z should be the function of x and y only` is incorrect as z should be the homogeneous function of x and y not non-homogeneous functions.