Homogeneous function | Degree | ||
A. | \(f(x,y)=\frac{x^\frac{1}{3}+y^\frac{1}{3}}{x^\frac{1}{2}+y^\frac{1}{2}}\) | I. | 3 |
B. | \(f(x,y)=\frac{x+y}{\sqrt{x}+\sqrt{y}}\) | II. | \(\frac{1}{2}\) |
C. | \(f(x,y)=\frac{x^4+y^4}{x+y}\) | III. | 1 |
D. | \(f(x,y)=\frac{\sqrt{x^3+y^3}}{\sqrt{x}+\sqrt{y}}\) | IV. | \(-\frac{1}{6}\) |
Let $f: [0, \infty) \to \mathbb{R}$ be a differentiable function such that $f(x) = 1 - 2x + \int_0^x e^{x-t} f(t) \, dt$ for all $x \in [0, \infty)$. Then the area of the region bounded by $y = f(x)$ and the coordinate axes is