T/F: The set: $\{(x,y): \sin(x^{2012} +y^3) + x^2 + y^4 \le 1\}$ is a compact set in $\mathbb{R}^2$.

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T/F: The set: $\{(x,y): \sin(x^{2012} +y^3) + x^2 + y^4 \le 1\}$ is a compact set in $\mathbb{R}^2$.

I think it is false since I don't believe the set is closed nor bounded? Is that correct?