Limit function (x^2-4)/(x-2) as approaches 2

 

To find the limit of the function

$$\lim_{x \to 2} \frac{x^2 - 4}{x - 2}$$

Step 1: Factor the numerator

$$x^2 - 4 = (x - 2)(x + 2)$$

Step 2: Cancel common factors

$$\frac{(x - 2)(x + 2)}{x - 2} = x + 2 \quad \text{for } x \ne 2$$

Step 3: Take the limit of the simplified function

$$\lim_{x \to 2} x + 2 = 4$$

Final Answer:

$$\boxed{4}$$