Determine the limit of the function as x approaches 4: 2) $\lim _{x \rightarrow 4} f(x) \frac{x-4}{\sqrt{x}-2}$

Step 1 ：Determine the limit of the function as x approaches 4: \(\lim _{x \rightarrow 4} f(x) \frac{x-4}{\sqrt{x}-2}\)

Step 2 ：The function seems to be undefined at x=4, as the denominator becomes 0. However, this might be a case of removable discontinuity, where the function is undefined at a certain point, but the limit exists.

Step 3 ：To find the limit, we can try to simplify the function and cancel out the term that is causing the function to be undefined at x=4.

Step 4 ：x = x

Step 5 ：f = (x - 4)/(sqrt(x) - 2)

Step 6 ：limit = 4

Step 7 ：The limit of the function as x approaches 4 is 4. This means that as x gets closer and closer to 4, the value of the function gets closer and closer to 4.

Step 8 ：Final Answer: \(\boxed{4}\)