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Non-analytic smooth function
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===Definition of the function=== [[Image:Non-analytic smooth function.png|right|frame|The non-analytic smooth function ''f''(''x'') considered in the article.]] Consider the function :<math>f(x)=\begin{cases}e^{-\frac{1}{x}}&\text{if }x>0,\\ 0&\text{if }x\le0,\end{cases}</math> defined for every [[real number]] ''x''.
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