`f(x,y) = 2ln(xy)` Determine whether the function is homogenous and if it is, determine its degree

Sunday, December 27, 2015

$\displaystyle{f{{\left({x},{y}\right)}}}={2}{\ln{{\left({x}{y}\right)}}}$ Determine whether the function is homogenous and if it is, determine its degree

Given

$\displaystyle{f{{\left({x},{y}\right)}}}={2}{\ln{{\left({x}{y}\right)}}}={2}{\ln{{\left({x}\right)}}}+{2}{\ln{{\left({y}\right)}}}$

to check whether the given function is homogenous

then it has to be

$\displaystyle{f{{\left({t}{x},{t}{y}\right)}}}={{t}}^{{n}}{f{{\left({x},{y}\right)}}}$

so ,

$\displaystyle{f{{\left({t}{x},{t}{y}\right)}}}={2}{\ln{{\left({t}{x}\cdot{t}{y}\right)}}}={2}{\ln{{\left({{t}}^{{2}}{x}{y}\right)}}}={2}{\ln{{\left({{t}}^{{2}}\right)}}}+{2}{\ln{{\left({x}{y}\right)}}}$

$\displaystyle={4}{\ln{{\left({t}\right)}}}+{2}{\ln{{\left({x}\right)}}}+{2}{\ln{{\left({y}\right)}}}$

which is not of the form $\displaystyle{f{{\left({t}{x},{t}{y}\right)}}}={{t}}^{{n}}{f{{\left({x},{y}\right)}}}$

so the function is not Homogenous.

Blog

Sunday, December 27, 2015

$\displaystyle{f{{\left({x},{y}\right)}}}={2}{\ln{{\left({x}{y}\right)}}}$ Determine whether the function is homogenous and if it is, determine its degree

No comments:

Post a Comment

Thomas Jefferson's election in 1800 is sometimes called the Revolution of 1800. Why could it be described in this way?

Sunday, December 27, 2015

Determine whether the function is homogenous and if it is, determine its degree

No comments:

Post a Comment

Thomas Jefferson&#39;s election in 1800 is sometimes called the Revolution of 1800. Why could it be described in this way?

$\displaystyle{f{{\left({x},{y}\right)}}}={2}{\ln{{\left({x}{y}\right)}}}$ Determine whether the function is homogenous and if it is, determine its degree

Thomas Jefferson's election in 1800 is sometimes called the Revolution of 1800. Why could it be described in this way?