A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 5 years ago
if homogeneous find the degree of homogeneity
1) (x^2+y^2)^1/2
2) (x+y)^5 + x^5y^5
help plzz....:)
anonymous
 5 years ago
if homogeneous find the degree of homogeneity 1) (x^2+y^2)^1/2 2) (x+y)^5 + x^5y^5 help plzz....:)

This Question is Closed

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0add a "t" variable to each x and y...

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0[(tx)^2 + (ty)^2] ^ (1/2) [t^2x^2 + t^2y^2]^(1/2) [t^2(x^2 + y^2)]^(1/2) t^2^(1/2) = t right?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0is homo..and degree 1

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0(tx+ty)^5 + (tx)^5(ty)^5 (tx+ty)^5 + t^5(x^5y^5) I dont think that left hand part is going to be homo.... youd have to factor it out and see if a single "t" variable can be pulled from it... and I dont think it can

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0t^5x^5 +5t^4x^4ty +10txty +10txty +5txty +t^5y^5 yeah, its good.... if I did it right... its homo and t^5 degree

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0thanks i got the first one wasn't sure about the second!^_^

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0I used pascals triangle to determine the cooefficients for the ^5 part. and then realized that the xy variables all have exponents that equal ^5.... t^4 t^1 = t^5...and so on....

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0do you know how to show that eulers theorem holds for these equations?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0...breif me on eulers thrm ...whats it state again?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.023.9 Euler Theorem Consider a function f(x1, x2, x3,….,xn) that is homogeneous of degree r. Let us rewrite f(kx1, kx2, kx3,….,kxn) as f(w1, w2, w3,….,wn) where wi = kxi for i = 1, 2,..,n. By Definition 23.5.1 of the Total Differential we can write df = f1 dw1 + f2 dw2 + ….+ fi dwi +…... ……+ fn dwn. where each fi is the first order partial derivative with respect to wi. If we now divide by dk we get the following result: df = f1 dw1 + f2 dw2 + ….+ fi dwi +…... ……+ fn dwn. dk dk dk dk dk Since dwi = xi for each i = 1, 2, ….n we can refine the above result to dk df = f1 x1 + f2 x2 + ….+ fi xi +…... ……+ fn xn. * dk Recall that f(kx1, kx2, kx3,….,kxn) = kr f(x1, x2, x3,….,xn). Thus df = r k r1 f(x1, x2, x3,….,xn). ** dk Also since each fi = f/wi it follows from the Chain Rule that f/xi = f/wi wi/xi = k f/wi *** Substituting ** into * we get r kr1 f(x1, x2, x3,….,xn) = f1 x1 + f2 x2 + ….+ fi xi +…... ……+ fn xn Multiplying both sides by k we get r kr f(x1, x2, x3,….,xn) = kf1 x1 + kf2 x2 + ….+ kfi xi +…... ……+ kfn xn Substituting *** into the above equation we get r kr f(x1, x2, x3,….,xn) = f/x1 x1 + f/x2 x2 + ….+ f/xi xi +…... ……+ f/xn xn Hence the result in the next theorem. 23.9.1 Euler’s Theorem Assume that f(x1, x2, x3,….,xn) is a homogeneous function of degree r. Then r f(x1, x2, x3,….,xn) = f1(x) x1 + f2(x) x2 + ……….+ fi(x) xi +…..……+ fn(x) xn where x = (x1, x2, x3,….,xn). The right hand side is the sum of the products of the partial derivative fi(x) and the variable xi . The left hand side is simply r times the function f(x). In the case of n = 2 variables, Euler’s Theorem for a homogeneous function f(x1, x2) of degree r is given by r f(x1, x2) = f1(x) x1 + f2(x) x2

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0this is from my notes but im having a hard time understanding and applying it....

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0they use "k" instead of "t"; r is the value of the "degree". that "i" just means that with each iteration of the function we get a certain value....

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0fi(x) seems to mean [f(x)]^i right?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0r f(x, y) = f^1(x) x + f^2(x) y is all I can make out of that, and dont even know if I m right :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yeah i get that just not sure how to apply it...i think it jus means i= variable in question....ok thanks for your help....:)
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.