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Let $G\in C(\mathbb R)$ then $\lim_{N\to +\infty}\frac{G(x-\frac{1}{N})-G(x)}{-\frac{1}{N}}=G'(x)$?

I have a doubt about the sign in front of $G'$, it is a $+$ or a $-$? Thanks to everyone

user495333
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1 Answers1

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The definition of the derivative is usually stated as:

$$ G'(x) = \lim \limits_{h \rightarrow 0} \frac{G(x+h)-G(x)}{h} $$

If we replace $h$ by $-\frac{1}{N}$, we get the expression in your question. So, the sign in front of $G'$ is indeed positive.

Sambo
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