Find the limit.
$\lim_{x\rarr2}\sqrt{x^2+5}$

• A. $0$
• B. $2$
• C. $3$
• D. $5$

Answer: (C)

Verified step by step guidance

1. Identify the type of limit problem: This is a direct substitution limit problem where you need to find the limit of a function as x approaches a specific value.
2. Understand the function: The function given is \( \sqrt{x^2 + 5} \). You need to evaluate this function as \( x \) approaches 2.
3. Apply direct substitution: Since the function \( \sqrt{x^2 + 5} \) is continuous at \( x = 2 \), you can directly substitute \( x = 2 \) into the function.
4. Substitute \( x = 2 \) into the function: Replace \( x \) with 2 in the expression \( \sqrt{x^2 + 5} \) to get \( \sqrt{2^2 + 5} \).
5. Simplify the expression: Calculate \( 2^2 \) and add 5, then take the square root of the result to find the limit.