Question

The values f(x) of a function f can be made arbitrarily large by taking x sufficiently close to 2 but not equal to 2. Which of the following statements must be true?

A) f(2) does not exist.
B) f is continuous at x=2.
C) limx→2 f(x) = ∞
D) limx→∞ f(x) = 2

Answer 1

The correct statement is C) limx→2 f(x) = ∞.

Step-by-step explanation:

In this case, the correct statement must be C) limx→2 f(x) = ∞

The given information states that the values of the function f(x) can be made arbitrarily large by taking x sufficiently close to 2 but not equal to 2. This implies that as x approaches 2, the function approaches infinity. So, the limit of f(x) as x approaches 2 is infinity.

Statements A and B cannot be determined from the given information. And statement D, limx→∞ f(x) = 2, is also not correct because the function becomes arbitrarily large as x approaches 2, not as x approaches infinity.