Apentix/AP Calculus AB/Ap calc ab u1/Question
AP Calculus ABhardmcq1 pt

The function f(x) = x^2sin(1/x) has an infinite discontinuity at x = 0.

A.D) The function has a removable discontinuity at x = 0.
B.C) The limit of f(x) as x approaches 0 exists.
C.B) The function is not defined at x = 0.
D.A) This is the primary reason the limit of f(x) as x approaches 0 does not exist.

Explanation

Core Concept

The function f(x) = x^2sin(1/x) has an infinite discontinuity at x = 0 because as x approaches 0, the function oscillates between positive and negative values. This means that the limit of f(x) as x approaches 0 does not exist. Option A is correct because the function has an infinite discontinuity at x = 0. Option B is incorrect because the function is defined at x = 0. Option C is incorrect because the limit of f(x) as x approaches 0 does not exist.

Correct Answer

A

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