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Let $f$ be a function defined on an open interval $(a,b)$ which has continuous derivatives of order $1,2, \dots , n-1$, and there is a point $c \in (a,b)$ such that $f(c), f^{{1}}(c), \dots , f^{(n-1)}(c)$ are all $0$. However $f^{n}(c)$ is not $0$ and we can assume that $f^{n}(x) > 0$ for $x \in (a,b)$, however no assumptions about the continuity of $f^{(n)}(x)$ are made. In this case is it true that $\lim_{x\to c}\frac{f(x)}{(x-c)^n} = \frac{f^{(n)}(c)}{n!}$?

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    That's L'Hôpital to you.2010-08-06
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    @Noldorin: that's my preferred spelling too. From [MathWorld](http://mathworld.wolfram.com/LHospitalsRule.html): *Note that l'Hospital's name is commonly seen spelled both "l'Hospital" (e.g., Maurer 1981, p. 426; Arfken 1985, p. 310) and "l'Hôpital" (e.g., Maurer 1981, p. 426; Gray 1997, p. 529), the two being equivalent in French spelling.*2010-08-06
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    @Isaac: Yeah. The circumflex accent represents a missing 's', and is the more common (less archaic) spelling... It represents pronunciation better for sure.2010-08-06

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