AP Calculus ABmediummcq1 pt

The function f(x) = |x|/x has a discontinuity at x = 0.

A.C) The function is continuous at x = 0.

B.D) The limit of f(x) as x approaches 0 is 0.

C.A) This is the primary reason the limit of f(x) as x approaches 0 does not exist.

D.B) The function is not defined at x = 0.

Explanation

Core Concept

The function f(x) = |x|/x is not continuous at x = 0 because it is undefined at this point. The primary reason the limit of f(x) as x approaches 0 does not exist is that the function is discontinuous at this point. Options B and D are not supported by the data, as the function is undefined at x = 0 and the limit does not exist. Option C is incorrect because the function is not continuous at x = 0.

Correct Answer

CA) This is the primary reason the limit of f(x) as x approaches 0 does not exist.

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