If it exists, what is:

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If it exists, what is:

Mathematics
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\[\lim_{h \rightarrow 0}\frac{ f(3+h)-f(3) }{ h }\]
What is the function f ?
Function f? There should be a definition for f(x)?

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I'm sorry @iamMJae. You're question is not fully written. You need to have some function. If you want to go ahead and sub x=0, you'll get a 0 in the denominator which makes it undefined.
That's all we got. All the question says: If it exists, what is: \[\lim_{h \rightarrow 0}\frac{ f(3+h)-f(3) }{ h }\]
if what exists?
If I understand the question correctly, it's the limit. "If the limit exists..."
does it exist?
do you know the definition of the derivative (if it exist)
can a limit exist without a function?
well the question says what is the limit if it exists and if exists then we know another we know the value to be...
that is if \[\lim_{h \rightarrow 0}\frac{g(a+h)-g(a)}{h} \text{ exists } \\ \text{ we call this value } \frac{dg(x)}{dx}|_{x=a}\]
and that is all I can do without knowing what g actually is
or f in your case
It simply is \(f'(3)\)
@mukushla How did it become \[f'(3)\] ?
He used definition of derivative
This is what I gave you above except your f is my g and your 3 is my a
@freckles The derivative is supposed to be the limit? I'm now confused.
The derivative of g at a is the way I defined it above
But we're looking for the limit.
http://tutorial.math.lamar.edu/Classes/CalcI/DefnOfDerivative.aspx see the definition.. Though I already wrote it above
@iamMJae you don't have the function, but question says "if the limit exists", this means if the limit exists the value of it will be \(f'(3)\), whatever \(f(x)\) might be.
I'm still quite confused but... We can conclude this problem with, "If it exists, the limit is \[f'(3)\]"?
There should be a little more info here imo. We have to assume there is some function f, with some formula to calculate values of it. You then could calculate the given limit. If THAT exists, it is, by definition, the derivative of f in x=3, so yes, if this limit exists, it is \(f'(3)\)
The question is a check for the understanding of the definition of derivatives. It gave the definition of the derivative and see if the students can recognize it, so there is nothing unclear about the question. @mukushla gave a direct answer.
@mathmate: I'm sure the original question was clear, it's just that @iamMJae was a little terse in her question here.

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