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Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.

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How to determine whether a multivariate function is bounded or not

Suppose there is a function $f:\mathbb{R}_+^n\mapsto \mathbb{R}$. Are there any systematic ways to determine whether the range of $f$ is bounded or not? For example, there is a function $f(x,y)=-x^2+ …