Final answer:
The likely true statement that Lim(x->3) f(x) = 8 is based on the differentiability of the function at x = 3, which implies continuity at that point.
Step-by-step explanation:
The student's question about the differentiable function f indicates that they are learning about the properties of functions and their limits. Given that f(3) = 8 and f'(3) = 5, it's stated that as x approaches 3, the limit of f(x) is 8. Since the function is differentiable at x = 3, this would imply that the function is also continuous at x = 3.
Thus, the statement Lim(x→3) f(x) = 8 is likely to be true, not false. However, without additional information about the behavior of f(x) near x = 3, we cannot conclusively determine if any other conditions might lead to a different conclusion.