Question

The existence of a limit at c affects the value of the function at c
a)True
b)False

Answer 1

The existence of a limit at c can affect the value of a function.

Step-by-step explanation:

The correct option is a) True.

The existence of a limit at c can affect the value of a function. When the limit of a function exists at c, it means that the function approaches a certain value as x approaches c. This can help determine the behavior and value of the function at c or in its surrounding neighborhood.

For example, let's consider the function f(x) = (x^2 - 1) / (x - 1). This function is undefined at x = 1 because of the division by zero issue. However, if we take the limit of the function as x approaches 1, we find that lim(x→1) f(x) = 2. This indicates that the function has a removable discontinuity at x = 1, and the value at x = 1 is 2.