Euler's Theorem on Homogeneous Functions — Study Resources & PYQs
Euler's theorem and its applications to homogeneous functions.
- Estimated study time: 30 minutes
Study resources
- Euler's Theorem on Homogeneous Functions (Article) — Clear statement, proof and the 2- and 3-variable forms with the relation between partial derivatives and degree. GATE-oriented.
- Euler's Theorem on Homogeneous Functions (Article) — Definition of homogeneous functions, statement and step-by-step proof of Euler's theorem with solved examples.
Euler's Theorem on Homogeneous Functions previous year questions
- (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 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 na…
- (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…
Taught in these subjects
- ENGINEERING MATHEMATICS-I — BMAT11 · Government College of Engineering and Technology, Jammu
- ENGINEERING MATHEMATICS-I — BMAT11 · Government College of Engineering and Technology, Jammu
- Engineering Mathematics-I — BMAT11 · Government College of Engineering and Technology, Jammu
- Engineering Mathematics-I — BST1101 · Government College of Engineering and Technology, Jammu
- Engineering Mathematics-I — BST1101 · Government College of Engineering and Technology, Jammu