Expert: Paul Klarreich - 11/22/2009

Question
Dear Paul, please help me how to solve following problems. Thanks:)

1. Determine whether the following function is homogeneous and, if so, to what degree: f(x,y)= square root of(x^2-y^2)

2) Use L’Hôpital’s rule to show that lim(x→∞)x^n/e^x=0

3) Given a production function Q(a,b), how to express the isoquant for an output level of Qˆ algebraically?

Answer
Questioner: Geli
Country: United States
Category: Advanced Math
Private: No
Subject: Homogenous, L’Hôpital’s rule
Question: Dear Paul, please help me how to solve following problems. Thanks:)

1. Determine whether the following function is homogeneous and, if so, to what degree: f(x,y)= square root of(x^2-y^2)

A. Write out the definition of homogeneous.
B. Apply it.  Compute f(ax,ay) and see what you get.


2) Use L’Hôpital’s rule to show that lim(x→∞)x^n/e^x=0

Apply it n times.  That should do it.


3) Given a production function Q(a,b), how to express the isoquant for an output level of Qˆ algebraically?

READ MY INSTRUCTIONS, PLEASE.  No special jargon!