- #1

Berrius

- 19

- 0

## Homework Statement

Show that [itex]D = { (x,y,z) \in \mathbb{R}^{3} | 7x^2+2y^2 \leq 6, x^3+y \leq z \leq x^2y+5y^3}[/itex] is bounded.

## Homework Equations

Definition of bounded:[itex]D \subseteq \mathbb{R}^{n}[/itex] is called bounded if there exists a M > 0 such that [itex]D \subseteq \{x \in \mathbb{R}^{n} | ||x|| \leq M\}[/itex]

## The Attempt at a Solution

I have to find a M such that [itex]D \subseteq \{(x,y,z) \in \mathbb{R}^{3} | x^2 + y^2 + z^2 \leq M\}[/itex]. I thought of just picking a very high M, say 999999. But how do I show it works?