Apentix/AP Calculus AB/Unit 1: Limits and Continuity/Question
AP Calculus ABmediummcq1 pt

Let h(x) = 2x + 1 for x ≠ 3, with h(3) = 8. Which statement explains why h is not continuous at x = 3?

A.h(3) is undefined.
B.The limit of h(x) as x approaches 3 does not exist.
C.The limit of h(x) as x approaches 3 is 7, but h(3) = 8.
D.h is not defined for x < 3.

Explanation

Core Concept

For x ≠ 3, h(x) = 2x + 1, so the limit as x approaches 3 is 7. Continuity at a point requires the limit to equal the function value, but h(3) = 8. Both the value and the limit exist, so the failure is exactly their mismatch, a removable break that redefining h(3) = 7 would repair.

Correct Answer

CThe limit of h(x) as x approaches 3 is 7, but h(3) = 8.

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