Question Bank • QB_EXP_EM_PD_010 MCQ • 1 Mark

Section 1: Engineering Mathematics

Calculus: Partial Derivatives & Maxima-Minima

Subtopic: Euler's theorem on homogeneous functions

Question Statement:

If $u(x, y)$ is a homogeneous function of degree $n = 4$ in $x$ and $y$, the value of $x \frac{\partial u}{\partial x} + y \frac{\partial u}{\partial y}$ is equal to:

Options:

  • (A) 4u
  • (B) 3u
  • (C) 12u
  • (D) 0

Answer Key:

A

Step-by-Step Solution & Explanation

According to Euler's Theorem for homogeneous functions of degree $n$: $x \frac{\partial u}{\partial x} + y \frac{\partial u}{\partial y} = n u$ Given $n = 4$, the value is $4u$.
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