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

Tuesday, July 21, 2015

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

A function $\displaystyle{f{{\left({x},{y}\right)}}}$ is called homogenous (homogeneous) of degree $\displaystyle{n},$ if for any $\displaystyle{x},$ $\displaystyle{y}$ we have $\displaystyle{f{{\left({t}{x},{t}{y}\right)}}}={{t}}^{{n}}{f{{\left({x},{y}\right)}}}.$

The given function is homogenous of degree 0, because

$\displaystyle{f{{\left({t}{x},{t}{y}\right)}}}={2}{\ln{{\left(\frac{{{t}{x}}}{{{t}{y}}}\right)}}}={2}{\ln{{\left(\frac{{x}}{{y}}\right)}}}={f{{\left({x},{y}\right)}}}={{t}}^{{0}}{f{{\left({x},{y}\right)}}}.$

The difficulty is that this function is not defined for all $\displaystyle{x}$ and $\displaystyle{y}.$ The above equality is true for all $\displaystyle{x}$ and $\displaystyle{y}$ for which it has sense.

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Tuesday, July 21, 2015

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

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

Tuesday, July 21, 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?

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