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