Apentix/AP Calculus AB/Unit 1: Limits and Continuity/Question
AP Calculus ABhardmcq1 pt

Which of the following statements about the function f(x) = (x² - 4)/(x - 2) is true?

A.B) The primary reason the limit of f(x) as x approaches 2 exists is that the function is continuous at this point.
B.A) The function is continuous at x = 2, but the limit of f(x) as x approaches 2 does not exist.
C.D) The function is continuous at x = 2, and the limit of f(x) as x approaches 2 also exists.
D.C) The function is not continuous at x = 2, but the limit of f(x) as x approaches 2 exists.

Explanation

Core Concept

The function f(x) = (x² - 4)/(x - 2) is not continuous at x = 2 because it is undefined at this point, but the limit of f(x) as x approaches 2 exists. Option A is incorrect because the function is not continuous at x = 2. Option B is incorrect because the function is not continuous at x = 2. Option D is incorrect because the function is not continuous at x = 2.

Correct Answer

DC) The function is not continuous at x = 2, but the limit of f(x) as x approaches 2 exists.

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