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

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.