Question

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

• A. a
• B. 0.0
• C. 5
• D. non-existent

Answer 1

The correct option is D non-existent

The given function is defined only at x = a. The value of the function at x = a is 5. When we are finding the limit of the function, we are not concerned about the value of the function at a, 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.