To evaluate the limit

\[
\lim_{h \to 0} \frac{f(x+h) - f(x)}{h},
\]

we recognize that this limit is the definition of the derivative of the function \(f(x)\) at the point \(x\). Thus, the limit evaluates to \(f'(x)\), which is the derivative of \(f(x)\) with respect to \(x\).

The specific value of the limit depends on the form of the function \(f(x)\). If you provide the function \(f(x)\), I can calculate the exact value of the derivative at the point \(x\). 

Would you like to provide the function \(f(x)\) or go over an example? 

Here are some related questions:
1. How do we find the derivative of \(f(x) = x^2\) using this limit definition?
2. What is the derivative of trigonometric functions like \(f(x) = \sin(x)\)?
3. How does the derivative change if the function \(f(x)\) is a polynomial?
4. What is the physical interpretation of the derivative in terms of velocity and acceleration?
5. How can you check if the limit definition correctly gives the derivative?

**Tip:** When using the limit definition to find a derivative, expanding \(f(x+h)\) using series expansion or known identities can simplify the process significantly.

Learn how to evaluate the limit \( \lim_{h \to 0} \frac{f(x+h) - f(x)}{h} \) to find the derivative of a function \( f(x) \). This problem discusses the fundamental theorem of calculus, explaining the concept and its application. Suitable for undergraduate students and those studying calculus.

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