The limit $\displaystyle \lim_{x \to 0} x^2 \sin(1/x)$ A. does not exist because no matter how close $x$ gets to $0$, there are some $x$'s near $0$ for which $\sin(1/x) = 1$ and other $x$'s near $0$ for which $\sin(1/x) = -1$. B. does not exist because the function values oscillate around $0$. C. does not exist because $1/0$ is undefined. D. is equal to $0$. E. is equal to $1$. In the answer box below, explain your reasoning for the choice you made above. Use complete sentences and correct grammar, spelling, and punctuation. Be specific and detailed. Write as if you were explaining the answer to someone else in class.

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