Question

Let f(x) = 2x². This function is not defined at x = 0. Does this function have a limit at x = 0?

1) True
2) False

Answer 1

It is false to say that f(x) = 2x² is not defined at x = 0; it is indeed defined and the limit as x approaches 0 exists and equals 0.

Step-by-step explanation:

The statement saying that the function f(x) = 2x² is not defined at x = 0 is false. In fact, this function is well-defined at x = 0, and we can find its value by simply substituting 0 into the equation:

f(0) = 2(0)² = 0.

Therefore, the function f(x) = 2x² is defined at x = 0 and indeed has a limit at this point. The limit as x approaches 0 for this function is:

lim (x -> 0) f(x) = lim (x -> 0) 2x² = 2(0)² = 0.

This function is a simple quadratic function, and as x approaches any real number value, including zero, the function approaches a finite value, which is the limit of the function at that point. So, the limit of f(x) at x = 0 is true.