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iamMJae
 one year ago
If it exists, what is:
iamMJae
 one year ago
If it exists, what is:

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iamMJae
 one year ago
Best ResponseYou've already chosen the best response.1\[\lim_{h \rightarrow 0}\frac{ f(3+h)f(3) }{ h }\]

Zale101
 one year ago
Best ResponseYou've already chosen the best response.0What is the function f ?

iamMJae
 one year ago
Best ResponseYou've already chosen the best response.1Function f? There should be a definition for f(x)?

Zale101
 one year ago
Best ResponseYou've already chosen the best response.0I'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.

iamMJae
 one year ago
Best ResponseYou've already chosen the best response.1That's all we got. All the question says: If it exists, what is: \[\lim_{h \rightarrow 0}\frac{ f(3+h)f(3) }{ h }\]

iamMJae
 one year ago
Best ResponseYou've already chosen the best response.1If I understand the question correctly, it's the limit. "If the limit exists..."

freckles
 one year ago
Best ResponseYou've already chosen the best response.1do you know the definition of the derivative (if it exist)

nincompoop
 one year ago
Best ResponseYou've already chosen the best response.1can a limit exist without a function?

freckles
 one year ago
Best ResponseYou've already chosen the best response.1well the question says what is the limit if it exists and if exists then we know another we know the value to be...

freckles
 one year ago
Best ResponseYou've already chosen the best response.1that is if \[\lim_{h \rightarrow 0}\frac{g(a+h)g(a)}{h} \text{ exists } \\ \text{ we call this value } \frac{dg(x)}{dx}_{x=a}\]

freckles
 one year ago
Best ResponseYou've already chosen the best response.1and that is all I can do without knowing what g actually is

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0It simply is \(f'(3)\)

iamMJae
 one year ago
Best ResponseYou've already chosen the best response.1@mukushla How did it become \[f'(3)\] ?

freckles
 one year ago
Best ResponseYou've already chosen the best response.1He used definition of derivative

freckles
 one year ago
Best ResponseYou've already chosen the best response.1This is what I gave you above except your f is my g and your 3 is my a

iamMJae
 one year ago
Best ResponseYou've already chosen the best response.1@freckles The derivative is supposed to be the limit? I'm now confused.

freckles
 one year ago
Best ResponseYou've already chosen the best response.1The derivative of g at a is the way I defined it above

iamMJae
 one year ago
Best ResponseYou've already chosen the best response.1But we're looking for the limit.

freckles
 one year ago
Best ResponseYou've already chosen the best response.1http://tutorial.math.lamar.edu/Classes/CalcI/DefnOfDerivative.aspx see the definition.. Though I already wrote it above

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@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.

iamMJae
 one year ago
Best ResponseYou've already chosen the best response.1I'm still quite confused but... We can conclude this problem with, "If it exists, the limit is \[f'(3)\]"?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0There 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 \(f'(3)\)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.0The 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.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@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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