Question

If it exists, what is:

Answer 1

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

Answer 2

What is the function f ?

Answer 3

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

Answer 4

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.

Answer 5

That's all we got. All the question says:

If it exists, what is:

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

Answer 6

if what exists?

Answer 7

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

Answer 8

does it exist?

Answer 9

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

Answer 10

can a limit exist without a function?

Answer 11

well the question says what is the limit if it exists and if exists then we know another we know the value to be...

Answer 12

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

Answer 13

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

Answer 14

or f in your case

Answer 15

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

Answer 16

@mukushla How did it become \[f'(3)\] ?

Answer 17

He used definition of derivative

Answer 18

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

Answer 19

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

Answer 20

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

Answer 21

But we're looking for the limit.

Answer 22

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

Answer 23

@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.

Answer 24

I'm still quite confused but...

We can conclude this problem with, "If it exists, the limit is \[f'(3)\]"?

Answer 25

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 \(f'(3)\)

Answer 26

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.

Answer 27

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