The function f(x) = x² sin(1/x) is defined for all x ≠ 0. Which of the following statements about the function is true?

Core Concept

This question tests the student's understanding of continuity and discontinuity. The function has a discontinuity at x = 0 due to the oscillating nature of the sine function and the increasing amplitude of the x² term. Option A is incorrect because the function is not continuous at x = 0. Option C is incorrect because the function does not approach ∞; rather, the oscillations become more rapid and extreme. Option D is incorrect because the function does not approach 0; it oscillates.