Question

A subset S ⊆ $\R^2$ is said to be bounded if there is an M > 0 such that |x| ≤ M and |y| ≤ M for all (x, y) ∈ S. Which of the following subsets of $\R^2$ is/are bounded ?

• A. ${(x, y) ∈ \R^2 : e^{x^2} + y^2 \le 4}$
• B. ${(x, y) ∈ \R^2 : x^4 + y^2 \le 4}$
• C. ${(x, y) ∈ \R^2 : |x| + |y| \le 4}$
• D. ${(x, y) ∈ \R^2 : e^{x^3} + y^2 \le 4}$

Answer 1

Answer: (A), (B), (C)

${(x, y) ∈ \R^2 : e^{x^2} + y^2 \le 4}$

Answer 2

The correct option is (A) : ${(x, y) ∈ \R^2 : e^{x^2} + y^2 \le 4}$, (B) : ${(x, y) ∈ \R^2 : x^4 + y^2 \le 4}$ and (C) : ${(x, y) ∈ \R^2 : |x| + |y| \le 4}$.