Question

The degree of the homogeneous function u (x, y, z) = (x/y) + (z/x) is _​

Answer 1

Step-by-step explanation:

A function f is called homogeneous of degree n, then it will satisfy the equation-

f(tx,ty,tz)=t

n

f(x,y,z)

f(x,y,z)=F(u)

Let,

p=tx

q=ty

r=tz

Therefore,

dt

d

(p,q,r)=nt

n−1

f(x,y,z)

∂p

∂f

dt

dp

+

∂q

∂f

dt

dq

+

∂r

∂f

dt

dr

=nt

n−1

F(u)(∵F(u)=f(x,y,z))

⇒x

∂p

∂f

+y

∂q

∂f

+z

∂r

∂f

=nt

n−1

F(u)

Substituting t=1, we get

x

∂x

∂f

+y

∂y

∂f

+z

∂z

∂y

=nF(u)