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

1. iamMJae

$\lim_{h \rightarrow 0}\frac{ f(3+h)-f(3) }{ h }$

2. Zale101

What is the function f ?

3. iamMJae

Function f? There should be a definition for f(x)?

4. 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.

5. iamMJae

That's all we got. All the question says: If it exists, what is: $\lim_{h \rightarrow 0}\frac{ f(3+h)-f(3) }{ h }$

6. nincompoop

if what exists?

7. iamMJae

If I understand the question correctly, it's the limit. "If the limit exists..."

8. nincompoop

does it exist?

9. freckles

do you know the definition of the derivative (if it exist)

10. nincompoop

can a limit exist without a function?

11. 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...

12. freckles

that is if $\lim_{h \rightarrow 0}\frac{g(a+h)-g(a)}{h} \text{ exists } \\ \text{ we call this value } \frac{dg(x)}{dx}|_{x=a}$

13. freckles

and that is all I can do without knowing what g actually is

14. freckles

15. nincompoop

16. anonymous

It simply is $$f'(3)$$

17. iamMJae

@mukushla How did it become $f'(3)$ ?

18. freckles

He used definition of derivative

19. freckles

This is what I gave you above except your f is my g and your 3 is my a

20. iamMJae

@freckles The derivative is supposed to be the limit? I'm now confused.

21. freckles

The derivative of g at a is the way I defined it above

22. iamMJae

But we're looking for the limit.

23. freckles

http://tutorial.math.lamar.edu/Classes/CalcI/DefnOfDerivative.aspx see the definition.. Though I already wrote it above

24. 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.

25. iamMJae

I'm still quite confused but... We can conclude this problem with, "If it exists, the limit is $f'(3)$"?

26. 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 $$f'(3)$$

27. 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.

28. ZeHanz

@mathmate: I'm sure the original question was clear, it's just that @iamMJae was a little terse in her question here.