`f(x,y) = x^3 -4xy^2 + y^3` Determine whether the function is homogenous and if it is, determine its degree

Friday, November 25, 2016

$\displaystyle{f{{\left({x},{y}\right)}}}={{x}}^{{3}}-{4}{x}{{y}}^{{2}}+{{y}}^{{3}}$ Determine whether the function is homogenous and if it is, determine its degree

Given,

$\displaystyle{f{{\left({x},{y}\right)}}}={{x}}^{{3}}-{4}{x}{{y}}^{{2}}+{{y}}^{{3}}$

to check whether it is homogenous or not

$\displaystyle{f{{\left({t}{x},{t}{y}\right)}}}={{\left({t}{x}\right)}}^{{3}}-{4}{t}{x}{{\left({t}{y}\right)}}^{{2}}+{{\left({t}{y}\right)}}^{{3}}={\left({{t}}^{{3}}\right)}{\left({{x}}^{{3}}-{4}{x}{{y}}^{{2}}+{{y}}^{{3}}\right)}$

so this is of the form

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

and so the function f(x,y) is homogenous,

$\displaystyle{f{{\left({t}{x},{t}{y}\right)}}}={\left({{t}}^{{3}}\right)}{\left({{x}}^{{3}}-{4}{x}{{y}}^{{2}}+{{y}}^{{3}}\right)}$

and the Degree $\displaystyle{n}={3}$

Blog

Friday, November 25, 2016

$\displaystyle{f{{\left({x},{y}\right)}}}={{x}}^{{3}}-{4}{x}{{y}}^{{2}}+{{y}}^{{3}}$ 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?

Friday, November 25, 2016

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?

$\displaystyle{f{{\left({x},{y}\right)}}}={{x}}^{{3}}-{4}{x}{{y}}^{{2}}+{{y}}^{{3}}$ 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?