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Find $$\lim_{x\to a} \frac{f(x)-f(a)}{(x-a)}$$ if $f(x)$ is derivable in the point $a$.

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Welcome to math.SE: since you are new, I wanted to let you know a few things about the site. In order to get the best possible answers, it is helpful if you say in what context you encountered the problem, and what your thoughts on it are; this will prevent people from telling you things you already know, and help them give their answers at the right level. Also, many find the use of imperative ("Prove", "Solve", etc.) to be rude when asking for help; please consider rewriting your post. –  Julian Kuelshammer Nov 11 '12 at 13:47
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Do you have any (perhaps trivial) thoughts/guesses? –  Berci Nov 11 '12 at 13:47
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Please, try to make the title of your question more informative. E.g., Why does $a<b$ imply $a+c<b+c$? is much more useful for other users than A question about inequality. From How can I ask a good question?: Make your title as descriptive as possible. In many cases one can actually phrase the title as the question, at least in such a way so as to be comprehensible to an expert reader. –  Julian Kuelshammer Nov 11 '12 at 13:47
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What is your definition of "$f(x)$ is derivable in the point $a$"? –  Dennis Gulko Nov 11 '12 at 13:56
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1 Answer

The answer to your question it is $f^{\prime}(a)$.

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And, this is just by definition. If it happened that $f'(a)$ was defined using an $h\to 0$ in the denominator, instead of $(x-a)$, then you also need the substitution $h:=x-a$. –  Berci Nov 11 '12 at 14:05
    
@Amr: I used the formatting $f^\prime (a)$. You can pick up a lot of formatting knowledge by hovering over a formatted expression and "right-clicking" - then click "show math as" then click on "TeX" and a pop-up window will appear with the formatted expression (which then needs to be enclosed in dollar signs for this site). –  amWhy Nov 11 '12 at 14:57
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