Final answer:
The statement that the limit of a function as x approaches a certain value 'a' is always equal to the function's value at 'a' is false, as they can be different in cases of removable discontinuities.
Step-by-step explanation:
The statement that when lim x→a f(x) exists, it always equals f(a) is false. The limit of a function as x approaches a value 'a' does not necessarily equate to the value of the function at that point, which is denoted by f(a). This is because the limit is concerned with the behavior of the function as it approaches 'a', not necessarily the function's value at 'a'. A common scenario where this difference is observed is in the case of a function with a removable discontinuity at x = a where the limit as x approaches 'a' might exist, but the function's value at 'a' could be different or undefined.