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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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Question about optimizing a given function by optimizing an approximation

Let $f$ be a real-valued function. Suppose I want to find a local maximum of $f$, but I decide to work with an ''approximation'' to $f$ --let us call it $g$. What is a suitable notion of ''approximati …
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