Final answer:
The statement is false. The limit of a function does not always equal the value of the function at a specific point.
Step-by-step explanation:
The statement is false. The limit of a function, lim f(x), represents the value that the function approaches as x approaches a specific value, but it does not necessarily equal f(a). In other words, the limit and the value of the function at a specific point can be different.
For example, consider the function f(x) = x^2. If we take the limit of f(x) as x approaches 2, we have lim x->2 (x^2) = 4. However, f(2) = 2^2 = 4. So, in this case, the limit and f(a) are equal.
However, there are cases where the limit and f(a) are not equal. For instance, consider the function g(x) = 1/x. If we take the limit of g(x) as x approaches 0, we have lim x->0 (1/x) = infinity (since the function approaches infinity as x gets closer to 0). However, g(0) is undefined. Therefore, the limit and f(a) can be different in general.