Question

when is it possible to redefine the value of a function f(c) so that the limit of f(x) as x approaches c is equal to f(c)?

Answer 1

To redefine the value of a function f(c) so that the limit of f(x) as x approaches c is equal to f(c), the function f(x) must be continuous at x = c.

Step-by-step explanation:

In order to redefine the value of a function f(c) so that the limit of f(x) as x approaches c is equal to f(c), the function f(x) must be continuous at x = c.

This means that the left-hand limit and the right-hand limit of f(x) as x approaches c must exist and be equal to f(c).

For example, if we have the function f(x) = x^2 and we redefine f(c) as c^2, then the limit of f(x) as x approaches c will be equal to f(c).