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

Friday, November 21, 2014

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

A function $\displaystyle{f{{\left({x},{y}\right)}}}$ is called homogeneous if for some integer $\displaystyle{n}$

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

The given function satisfies this condition with $\displaystyle{n}={0}:$

$\displaystyle{f{{\left({t}{x},{t}{y}\right)}}}={\tan{{\left(\frac{{{t}{x}}}{{{t}{y}}}\right)}}}={\tan{{\left(\frac{{x}}{{y}}\right)}}}={f{{\left({x},{y}\right)}}},$

and therefore it is homogeneous with the degree 0.

(although we have to note that for some x and y $\displaystyle{f{{\left({x},{y}\right)}}}$ is undefined)

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Friday, November 21, 2014

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

Friday, November 21, 2014

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?

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