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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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Conditional Integration of arbitrary function

Let $f(t) \in \mathbb{R}^+$, $g(t) \in \mathbb{R}^+$ be bounded and integrable functions, $A>0$ and $0 < \eta \leq 1$. If $h(t) = A\cdot f(t) - g(t)$, what needs to be the value of $A$ to satisfy \beg …