Final answer:
It is false that the existence of a limit at a particular point can be determined by examining the function only from one side; both sides must be considered.
Step-by-step explanation:
It is false that the existence of limx→4f(x) can be determined by examining f(x) only for values of x close to but greater than 4. For a limit to exist at x = 4, f(x) must approach the same value from both the left and the right side as x approaches 4. In other words, the behavior of f(x) must be examined as x approaches 4 from both sides, which includes values of x both less than and greater than 4. The limit existence requires checking the left-hand limit and the right-hand limit, and for both to be equal for the overall limit to exist.
The statement is False. To determine if limx→4f(x) exists, we cannot rely solely on the behavior of f(x) for values close to but greater than 4. The limit of a function at a point is determined by the behavior of the function for values approaching that point from both sides. Therefore, we need to examine the behavior of f(x) for values both less than and greater than 4 to determine if the limit exists.