Question

When the limit of f(x) as x approaches a exists, it always equals f(a).
a) True
b) False

Answer 1

The statement that the limit of f(x) as x approaches a always equals f(a) is false.

Step-by-step explanation:

The statement that the limit of f(x) as x approaches a always equals f(a) is false.

The existence of the limit of a function as x approaches a means that the function approaches a specific value as x gets arbitrarily close to a. However, that particular value may or may not be equal to f(a). The limit and the function value at a can be different in many cases.

For example, let's consider the function f(x) = |x| and a = 0. The limit of f(x) as x approaches 0 is 0, but f(0) is 0. So, the limit and the function value at a are not always equal.