(a) Verify Euler's theorem for the function : $z = 2x^2 + 3xy + 4y^2$…
Previous year question for Engineering Mathematics-I.
Question
(a) Verify Euler's theorem for the function : $z = 2x^2 + 3xy + 4y^2$.
(b) Find the radius of curvature at any point of the curve : $xy = c^2$.
(c) Find the nature of double points at the origin on the curve : $x^3 + y^3 - 4axy = 0$.
- Year: 2018
- Subject: Engineering Mathematics-I
Related pages
More PYQs on Euler's Theorem on Homogeneous Functions
- (a) Define a homogeneous function. State and prove Euler's theorem for homogeneous functions. (b) State Lagrange's mean value theorem. Discuss the applicabilit…
- (a) State and prove Euler's theorem for homogeneous functions of two variables of degree $n$. (b) Find the Taylor's series expansion of $f(x,y) = e^x \sin y$ a…
- Verify whether the following statements are true or false : (i) If : $z = \frac{x^2 + y^2}{x - y}$, then : $x \frac{\partial z}{\partial x} + y \frac{\partial…
- (a) Verify Green's theorem for $\oint_C (3x^2 - 8y^2) \, dx + (4y - 6xy) \, dy$, where $C$ is the boundary of the region defined by $x = 0$, $y = 0$ and $x + y…
- (a) Verify Green's theorem in the xy-plane for $\oint_C (2xy - x^2) dx + (x^2 + y^2) dy$ where $C$ is the boundary of the region enclosed by curves $y = x^2$ a…