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

The Correct Option is A, B, C

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