AP Calculus ABhardmcq1 pt

Which of the following statements is true about the function f(x) = x^2sin(1/x) as x approaches 0?

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

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

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

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

Explanation

Core Concept

As x approaches 0, the function f(x) = x^2sin(1/x) oscillates between positive and negative values. This means that the limit of f(x) as x approaches 0 does not exist. Option A is incorrect because the limit of f(x) as x approaches 0 does not exist. Option C is incorrect because the function does not have any infinite discontinuities. Option D is incorrect because the function has no removable discontinuities.

Correct Answer

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