The statement "y = xcosx" approaches zero as x approaches infinity is not equivalent to zero. This is because the limit of xcosx as x approaches infinity does not exist. The function xcosx oscillates between positive and negative values as x increases, never settling on a single value. To understand this, consider the behavior of the cosine function, which oscillates between -1 and 1. Multiplying this by x, which grows without bound as x approaches infinity, results in a function that does not converge to a single limit.

Data from mathematical analysis supports this conclusion. For instance, the limit of xcosx as x approaches infinity can be evaluated using L'Hôpital's rule or by examining the behavior of the function. L'Hôpital's rule states that if the limit of the quotient of two functions as x approaches a certain value is indeterminate, then the limit of the quotient is equal to the limit of the quotient of their derivatives. Applying this rule to xcosx, we find that the derivative of xcosx is cosx - xsinx, which does not approach zero as x approaches infinity. Alternatively, one can observe that as x becomes very large, the term x becomes dominant, and the cosine term oscillates between -1 and 1, causing the overall function to oscillate between positive and negative values without settling on a limit. This behavior is consistent with the mathematical definition of a limit not existing, as the function does not approach a single value as x approaches infinity.