Question

For homogeneous function the linear combination of rates of independent change along x and y axes is __________

(a) Integral multiple of function value

(b) no relation to function value

(c) real multiple of function value

(d) depends if the function is a polynomial

This question was posed to me in class test.

Question is taken from Euler’s Theorem in portion Partial Differentiation of Engineering Mathematics

Answer 1

Correct answer is (c) real multiple of function value

For explanation I would say: Euler’s theorem is nothing but the linear combination asked here, The degree of the homogeneous function can be a real number. Hence, the value is integral multiple of real number.