Find the limit.
$\(\lim\)_{x\(\rarr\)2}\(\sqrt{x^2+5}\)$

• A. $0$
• B. $2$
• C. $3$
• D. $5$

Answer: (C)

Verified step by step guidance

1. Identify the function for which you need to find the limit: \( \lim_{x \to 2} \sqrt{x^2 + 5} \).
2. Understand that the limit asks what value \( \sqrt{x^2 + 5} \) approaches as \( x \) gets closer to 2.
3. Substitute \( x = 2 \) directly into the function \( \sqrt{x^2 + 5} \) to check if the function is continuous at \( x = 2 \).
4. Calculate \( \sqrt{2^2 + 5} \) to see if the function is defined and continuous at \( x = 2 \).
5. Conclude that since the function is continuous at \( x = 2 \), the limit is simply the value of the function at \( x = 2 \).