Question

The graph of f(x) is given below. The limit of the function f(x) as x approaches 'a' is

• A. a
• B. 5
• C. 0
• D. None of these

Answer 1

The correct option is D

None of these

The given function is defined only at x = a. The value of the function at x = a is 5. Is this the limit of that function as x approaches a?

When we are finding the limit of a function, we are not concerned about the value of the function at that particular point, we care about how the function behaves at

points very close to a. We want to find what value the function approaches as x approaches a.

In this case, we cannot talk about how the function behaves around 'a' as the function itself is not defined in the neighborhood. So, we say the limit does not exist.