AP Calculus ABmediummcq1 pt

Based on the data, which of the following statements is true about the function f(x) = (x - 2)^2/(x - 2) as x approaches 2?

A.A) The limit of f(x) as x approaches 2 exists.
B.D) The function has a removable discontinuity at x = 2.
C.C) The function has an infinite discontinuity at x = 2.
D.B) The limit of f(x) as x approaches 2 does not exist.

Explanation

Core Concept

Based on the data, the function f(x) = (x - 2)^2/(x - 2) has a removable discontinuity at x = 2. As x approaches 2, the function approaches 2. The limit of the function as x approaches 2 exists. Option A is correct because the limit of f(x) as x approaches 2 exists. Option B is incorrect because the limit of f(x) as x approaches 2 exists. Option C is incorrect because the function does not have an infinite discontinuity.

Correct Answer

BD) The function has a removable discontinuity at x = 2.

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