AP Calculus ABhardmcq1 pt

Let f(x) = 1/x for x ≠ 0, with f(0) = 4. Which statement is true?

A.The limit of f(x) as x approaches 0 is 4.

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

C.The limit of f(x) as x approaches 0 is ∞.

D.f is continuous at x = 0.

Explanation

Core Concept

As x approaches 0 from the right, 1/x grows without bound, while from the left it drops without bound. Because the two sides run to opposite infinities, no single limiting value exists. Assigning f(0) = 4 cannot repair this infinite discontinuity, and the limit is neither 4 nor ∞.

Correct Answer

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

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