Final Answer:
The limit as x approaches 81 of √(x) is 9.
Step-by-step explanation:
In this limit problem, we are asked to find the limit as x approaches 81 of the square root of x. The expression can be written as limₓ → 81 √(x). To evaluate this limit, we substitute the value 81 for x into the expression:
limₓ → 81 √(x) = √(81) = 9.
Therefore, the limit as x approaches 81 of √(x) is 9.
This result can be understood by recognizing that the square root function is continuous, and as x approaches 81, the square root of x approaches the square root of 81, which is 9. The square root function is defined for non-negative real numbers, and in this case, the square root of 81 is a well-defined and finite value, resulting in a limit of 9.
In summary, the limit of √(x) as x approaches 81 is 9, and this is achieved by directly substituting the value of x into the expression, considering the continuity of the square root function and recognizing the well-defined nature of the square root of 81.