Chapter 8.3, Problem 2E

Describe the convex hull of the set S of points $\left[\begin{array}{c}x\\ y\end{array}\right]$ in ℝ² that satisfy the given conditions. Justify your answers. (Show that an arbitrary point p in S belongs to conv S.)

1. a. y = 1/x and x ≥ 1/2
2. b. y = sinx
3. c. y = x^1/2 and x ≥ 0