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 had been asked this question at a job interview.

My doubt is from Euler’s Theorem in chapter Partial Differentiation of Engineering Mathematics

Answer 1

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

For explanation: 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.