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The problem you're showing involves calculating the limit:

\[
\lim_{x \to 2} \sqrt{f(x)}
\]

Given the following information:

\[
\lim_{x \to 2} f(x) = 4
\]
\[
\lim_{x \to 2} g(x) = -2
\]
\[
\lim_{x \to 2} h(x) = 0
\]

We focus on the limit involving \( f(x) \).

### Solution:

Since the limit of \( f(x) \) as \( x \to 2 \) is 4, we can substitute that directly into the square root function:

\[
\lim_{x \to 2} \sqrt{f(x)} = \sqrt{\lim_{x \to 2} f(x)} = \sqrt{4} = 2
\]

Therefore, the solution is:

\[
\lim_{x \to 2} \sqrt{f(x)} = 2
\]

Would you like further explanation or have any questions?

### Relative questions:
1. What is the general rule for the limit of composite functions like \(\lim_{x \to a} \sqrt{f(x)}\)?
2. How does continuity of the square root function help in this problem?
3. What would happen if \(\lim_{x \to 2} f(x)\) were a negative number?
4. How could you apply similar limit properties to more complex functions, like \(\lim_{x \to 2} \ln(f(x))\)?
5. How does the limit of \(g(x)\) or \(h(x)\) affect the result?

### Tip:
When dealing with limits involving square roots, ensure the expression inside the square root is positive for the limit to be real.

What is the limit of sqrt(f(x)) as x approaches 2, given that lim f(x) = 4?

Learn how to compute the limit of sqrt(f(x)) as x approaches 2, using properties of limits and continuity. This step-by-step solution is ideal for students studying calculus and limits.

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