Final answer:
The limit of the expression \(\sqrt{x-5}\) as x approaches 9 is found by substituting 9 into the expression, which simplifies to the square root of 4, and thus the limit is 2.
Therefore, the correct answer is a) 2.
Step-by-step explanation:
The question is asking to determine the limit of the radical expression \(\sqrt{x-5}\) as x approaches 9. This type of problem involves the concept of limits in calculus, which helps us understand the behavior of functions as the input gets close to a certain value.
To determine the limit as x approaches 9 of √x-5, we can substitute 9 into the expression. So we have √9 - 5 = 3 - 5 = -2. The limit does not exist in this case since we get a negative value and none of the given options in the question are negative. Therefore, the correct answer is none of the above options.
To find the limit, substitute 9 for x in the expression:
\[ \lim_{x \to 9} \sqrt{x-5} = \sqrt{9-5} = \sqrt{4} \]
Since the square root of 4 is 2, the limit is:
\[ \lim_{x \to 9} \sqrt{x-5} = 2 \]
Therefore, the correct answer is a) 2.