The reason $\displaystyle \lim_{x \to 0} \sin(1/x)$ does not exist is A. because no matter how close $x$ gets to $0$, there are infinitely many $x$'s near $0$ for which $\sin(1/x) = 1$ and also infinitely many $x$'s near $0$ for which $\sin(1/x) = -1$. B. because the function values oscillate around $0$. C. because $1/0$ is undefined. D. all of the above. 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. Click this link for an interactive Google graph!