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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)?

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?

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

or f in your case

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

He used definition of derivative

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

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

But we're looking for the limit.