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The problem is asking what information the limit \(\lim_{x \to 2} \frac{f(x) - f(2)}{x - 2}\) provides about the function.

This expression is the definition of the **derivative** of \(f(x)\) at \(x = 2\). Therefore, the limit gives the **slope of the tangent line** to the function at \(x = 2\).

Thus, the correct answer is:
- **The slope of the tangent line to the function at \(x = 2\)**

Would you like more details or have any further questions?

Here are five related questions to expand your understanding:
1. What is the geometric interpretation of the derivative?
2. How do you compute the derivative of a function at a specific point?
3. What is the difference between the average rate of change and the instantaneous rate of change?
4. How can the existence of vertical or horizontal tangent lines be determined?
5. How do you find the equation of the tangent line at a given point?

**Tip:** The derivative gives the instantaneous rate of change of a function at any point. It can be seen as the slope of the tangent line to the curve at that point.

A Calculus student evaluated the limit as x approaches 2 for (f(x) - f(2)) / (x - 2). What knowledge about our function does the outcome provide?

Explore the concept of evaluating the limit lim (x → 2) (f(x) - f(2)) / (x - 2), which provides the slope of the tangent line to a function at x = 2. This problem demonstrates key ideas in calculus, including the derivative and instantaneous rate of change.

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