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You are given a function $f: \mathbb{R}\rightarrow \mathbb{R}$. Every derivative $\frac{d^n}{dx^n}(f(x)), \,n >0$ of the function is continuous.
Is there a function $g: \mathbb{R}\rightarrow \mathbb{R}$, for which every derivative $\frac{d^n}{dx^n}(g(x)), \,n >0$ is also continuous, such that:...
