iamMJae
  • iamMJae
If it exists, what is:
Mathematics
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katieb
  • katieb
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iamMJae
  • iamMJae
\[\lim_{h \rightarrow 0}\frac{ f(3+h)-f(3) }{ h }\]
Zale101
  • Zale101
What is the function f ?
iamMJae
  • iamMJae
Function f? There should be a definition for f(x)?

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Zale101
  • Zale101
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.
iamMJae
  • iamMJae
That's all we got. All the question says: If it exists, what is: \[\lim_{h \rightarrow 0}\frac{ f(3+h)-f(3) }{ h }\]
nincompoop
  • nincompoop
if what exists?
iamMJae
  • iamMJae
If I understand the question correctly, it's the limit. "If the limit exists..."
nincompoop
  • nincompoop
does it exist?
freckles
  • freckles
do you know the definition of the derivative (if it exist)
nincompoop
  • nincompoop
can a limit exist without a function?
freckles
  • freckles
well the question says what is the limit if it exists and if exists then we know another we know the value to be...
freckles
  • freckles
that is if \[\lim_{h \rightarrow 0}\frac{g(a+h)-g(a)}{h} \text{ exists } \\ \text{ we call this value } \frac{dg(x)}{dx}|_{x=a}\]
freckles
  • freckles
and that is all I can do without knowing what g actually is
freckles
  • freckles
or f in your case
nincompoop
  • nincompoop
anonymous
  • anonymous
It simply is \(f'(3)\)
iamMJae
  • iamMJae
@mukushla How did it become \[f'(3)\] ?
freckles
  • freckles
He used definition of derivative
freckles
  • freckles
This is what I gave you above except your f is my g and your 3 is my a
iamMJae
  • iamMJae
@freckles The derivative is supposed to be the limit? I'm now confused.
freckles
  • freckles
The derivative of g at a is the way I defined it above
iamMJae
  • iamMJae
But we're looking for the limit.
freckles
  • freckles
http://tutorial.math.lamar.edu/Classes/CalcI/DefnOfDerivative.aspx see the definition.. Though I already wrote it above
anonymous
  • anonymous
@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
  • iamMJae
I'm still quite confused but... We can conclude this problem with, "If it exists, the limit is \[f'(3)\]"?
ZeHanz
  • ZeHanz
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 \(f'(3)\)
mathmate
  • mathmate
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.
ZeHanz
  • ZeHanz
@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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