Question

This statement is true or false?Please justify your answer. `f(x,y)=sin((x²y)/(x³+y³))/(ln(x+y/x))` is a homogeneous function of degree 2.

Answer 1

See below.

Explanation:

A function `f(x,y)` is said to be homogeneous degree `k` iff

`f(lambda x,lambda y) = lambda^k f(x,y)`

`f(x,y)=sin((x²y)/(x³+y³))/(ln(x+y/x))` it is not a homogeneous degree `2` function because

`sin((x²y)/(x³+y³)) = sin((lambda^3 x^2y)/(lambda^3 x^3+lambda^3 y^3)) =sin((x²y)/(x³+y³))`

and `ln(x+y/x)` is not homogeneous at all