Which of the following is true regarding the function $f (x, y) = x^{4} sin \frac{x}{y}$ ?

Not homogenous

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Homogenous with degree 2

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Homogenous with degree 3

No worries! We‘ve got your back. Try BYJU‘S free classes today!

None of the above

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D None of the above
given function is $f (x, y) = x^{4} sin \frac{x}{y}$
Now, $f (k x, k y) = k^{4} x^{4} sin \frac{x}{y}$ ,
$\frac{f (k x, k y)}{f (x, y)} = k^{4}$
$∴$ the function is homogenous with Degree $4$ .

Suggest Corrections

Similar questions

F (x, y) = e^{y / x} + ln x - ln y

f (x, y) = \frac{1}{x + y}

f (x, y) = x^{3} l n [\sqrt{x + y} / \sqrt{x - y}]

f (x, y) = \frac{1}{x + y}

I

z = x y tan (\frac{y}{x})

x . \frac{\partial z}{\partial x} + y . \frac{\partial z}{\partial y} = z

I I

f (x, y) = \frac{1}{x^{2} y} + \frac{1}{x y^{2}} - \frac{log x - log y}{x^{3} + y^{3}}

Join BYJU'S Learning Program