Verify Eq (11) for the functions in Exercise 44 Data From Exercise 44 A function (x, y, z) is called homogeneous of degree n if (x, y, z) n (x, y, z) for all R Show that the following functions are homogeneous and determine their degree af af X 2 nf z af ax...

Eq 11 states that if f is homogeneous of degree n then X af af af ...

Verify Eq. (11) for the functions in Exercise 44. Data From Exercise 44 A function (x, y,

Question:

Verify Eq. (11) for the functions in Exercise 44.

af af X +2 =nf z af ax

Data From Exercise 44

A function ƒ(x, y, z) is called homogeneous of degree n if ƒ(λx, λy, λz) = λn ƒ(x, y, z) for all λ ∈ R.

Show that the following functions are homogeneous and determine their degree:

(a) f(x, y, z)= xy + xyz (c) f(x, y, z) = ln (2) (b) f(x, y, z) = 3x + 2y = 8z (d) f(x, y, z) = z

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

See More Books

Question Posted: Jan 16, 2024 09:01 AM

See More Questions

A function (x, y, z) is called homogeneous of degree n if (x, y, z) = n (x, y, z) for all R. Show that the following functions are homogeneous and determine their degree: (a) f(x, y, z) = xy + xyz...
A function f is called homogeneous of degree n if it satisfies the equation f (tx, ty) = t n f (x, y) for all t, where n is a positive integer and f has continuous second-order partial derivatives....
A function f(x) on Rn is called homogeneous of degree k if f(cx) = ci(x) for all scalars c. (a) If a Rn is a fixed vector, show that a linear form (x) = a . x = a1X1 +-----+ anxn is homogeneous of...
I need help with the 10-column worksheet. When I do the balance sheet the difference of my balance numbers do not equal my net income when it should. My net income is correct since the books states...
A variation of the indicator dilution method (see preceding problem) is used to measure total blood volume. A known amount of a tracer is injected into the bloodstream and disperses uniformly...
Determine the electrostatic potential energy and the kinetic energy of an electron in the ground state of the hydrogen atom.
The A992 steel bars are pin connected at $C$. If they each have a diameter of 2 in., determine the displacement of point $E$. 2 kip E B C -6 ft 6ft 10 ft 8 ft D
Some believe that iGAAP provides too many choices within its accounting guidance. Is this a possible concern in the area of cash flow reporting? Explain.
What about global supply chain uncertainty, risk and probabilities, hazards and gain insight into a variety of industries' risk. . A case study analysis requires you to investigate a business...
Suppose that is a function of x and y, where x = g(t, s), y = h(t, s). Show that tt is equal to fxx x at +2 () () at + fyy at + fx 22x + fy 12 12
Prove that if (x, y, z) is homogeneous of degree n, then Let F(t) = (tx, ty, tz) and calculate F'(1) using the Chain Rule. af + x af af z +2 =nf
A bank quotes the nominal annual rate of 6%, and it compounds interest every two months. What is the value of one dollar deposited in this bank after a year?
a. Solve the linear system $\mathbf{A x}=\mathbf{b}$ by using Cramer's rule. b. $\uparrow$ Repeat (a) in MATLAB. \(\mathbf{A}=\left[\begin{array}{cccc}3 & 2 & 0 & 0 \\ \frac{1}{2} & -\frac{4}{3}...
a. Solve the linear system $\mathbf{A x}=\mathbf{b}$ by using Cramer's rule. b. $\uparrow$ Repeat (a) in MATLAB. \(\mathbf{A}=\left[\begin{array}{cc}s^{2}+s+\frac{1}{3} & -\frac{1}{3} \\...
Briefly explain whether each of the following statements describes a change in supply or a change in quantity supplied. a. To take advantage of high prices for snow shovels during a snowy winter,...
Angelica collected data on peoples anxiety levels (x) and life satisfaction (y). The scores are below: a. Calculate the correlation for Angelicas data. b. What is the null hypothesis for these data?...
Cities like San Francisco and New York that require a driver to buy a city-issued taxi medallion before the driver can legally operate a taxi are shifting the supply curve for taxis to the left...
Tim Legler requires an estimate of the cost of goods lost by fire on March 9. Merchandise on hand on January 1 was $38,000. Purchases since January 1 were $72,000; freight-in, $3,400; purchase...
Suppose you need to answer any four of seven essay questions on a history test and you can answer them in any order. a. How many different question combinations are possible? b. What is the...
Assume equally likely outcomes. Determine the probability of having 3 girls in a 3-child family.
Assume equally likely outcomes. Determine the probability of having 1 girl and 3 boys in a 4-child family.
Assume equally likely outcomes. Determine the probability of having 2 girls and 2 boys in a 4-child family.
Started in 2008 by Ryan Holmes, Hootsuite is a social media management program. It has become a favourite tool for posting and monitoring social media content, plus it provides social listening,...
. A qualitative study of racial minority single mothers' work experiences. https://psycnet.apa.orq/record/2018 -49845-001 annotated bibliography Article One: List all important reference information...
Would you want to live in a society where crime rates were quite low because they were controlled by extremely harsh punishment, such as flogging for vandalism? Are criminals rational decision...

Verify Eq. (11) for the functions in Exercise 44. Data From Exercise 44 A function (x, y,

Question:

af af X +2 =nf z af ax

Step by Step Answer:

Eq 11 states that if f is homogeneous of degree n then X af af af ...View the full answer

Calculus

Students also viewed these Mathematics questions