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

AP Calculus ABeasymcq1 pt

The primary reason the function f(x) = 1/x is not continuous at x = 0 is that

A.The limit of f(x) as x approaches 0 does not exist.

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

C.The function has an infinite discontinuity at x = 0.

D.The function has a removable discontinuity at x = 0.

Explanation

Core Concept

The primary reason the function f(x) = 1/x is not continuous at x = 0 is that the limit of f(x) as x approaches 0 does not exist because as x approaches 0, f(x) approaches ∞. The function is not defined at x = 0, which is another reason the function is not continuous. Options C and D do not accurately describe the discontinuity of the function.

Correct Answer

AThe limit of f(x) as x approaches 0 does not exist.

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