fbpx
calculus online - Free exercises and solutions to help you succeed!

Homogeneous Functions – Homogeneous check to a constant function – Exercise 7041

Exercise

Determine if the following function:

f(x,y)=5

Is homogeneous.

Final Answer

 The function is homogeneous of degree 0

Solution

f(x,y)=5

Function f is called homogeneous of degree r if it satisfies the equation:

f(tx,ty)=t^rf(x,y)

for all t.

f(tx,ty)=

=5=

=t^0\cdot 5=

=t^0f(x,y)

We got

f(tx,ty)=t^0f(x,y)

Hence, by definition, the given function is homogeneous of degree 0.

Have a question? Found a mistake? – Write a comment below!
Was it helpful? You can buy me a cup of coffee here, which will make me very happy and will help me upload more solutions! 

Share with Friends

Leave a Reply