If lim_(x→a) [f(x) - g(x)] = 0, which of the following must be true?
Correct: A
The statement lim_(x→a) [f(x) - g(x)] = 0 means that as x approaches a, the difference f(x) - g(x) approaches 0. This implies that f(x) and g(x) approach the same value (or both approach the same infinite value). Therefore lim_(x→a) f(x) = lim_(x→a) g(x). Note that the individual limits need not exist as finite numbers (they could both be infinite), and f and g need not be defined at a or continuous at a. The key conclusion is that the limits of f and g at a are equal (in the extended real sense). Choice A is the correct answer.