Final answer:
The limit as x approaches 3 of the given function is equal to 8.
Step-by-step explanation:
The provided inequality, 3x - 1 ≤ f(x) ≤ x^2 - 3x + 8 for x ≥ 0, establishes a range for the function f(x). To determine the limit as x approaches 3, lim x→3 f(x), we exploit the continuity of the function. Evaluating f(x) at x = 3, we find f(3) = 3(3) - 1 = 8. Consequently, as x approaches 3, the limit lim x→3 f(x) equals 8. This result is derived from the substitution of x = 3 into the continuous function. The inequality provides a constraint on f(x), enabling the determination of the limit and establishing that it converges to 8 as x approaches 3 within the given context.