query: Prove that lim sin (1/x) as x-> 0 does not exist.
positive_passages.docid: 150601
positive_passages.text: The limit of $\sin(1/x)$ as $x\to 0$ does not exists
negative_passages.docid: 73786
negative_passages.text: Limit of $\frac{\sin(x+y)}{x+y}$ as $(x,y) \to (0,0)$
negative_passages.docid: 138583
negative_passages.text: What is the limit of $\lim\limits_{x→∞}\frac{\sin x}{x}$
negative_passages.docid: 106867
negative_passages.text: Limit of $\cos(x)/x$ as $x$ approaches $0$
negative_passages.docid: 2167
negative_passages.text: Find the limit $\lim\limits_{x\to \infty}(e^{-x}+2\cos3x)$, or show that it does not exist.
negative_passages.docid: 27423
negative_passages.text: Why does $\lim_{x\to 0^+} x^{\sin x}=1$?
negative_passages.docid: 122990
negative_passages.text: How can I prove that $\lim\limits_{n\to\infty}\frac{n+\sin n}{n+1} = 1$
negative_passages.docid: 122301
negative_passages.text: Evaluating and proving $\lim\limits_{x\to\infty}\frac{\sin x}x$
negative_passages.docid: 10428
negative_passages.text: Proving that $\lim\limits_{x\to\infty}f'(x) = 0$ when $\lim\limits_{x\to\infty}f(x)$ and $\lim\limits_{x\to\infty}f'(x)$ exist
negative_passages.docid: 135700
negative_passages.text: Show that $\lim_{n \to \infty} (1/n)\sum_{i=1}^n f(x_i)$ exists
negative_passages.docid: 29213
negative_passages.text: Limit of 1/x as x approaches infinity
negative_passages.docid: 151329
negative_passages.text: Showing $\lim_{(x,y) \to (0,0)} \sin (xy) / xy = 1$
negative_passages.docid: 28161
negative_passages.text: Solve $\lim_{x\to 0} \frac{\sin x-x}{x^3}$
negative_passages.docid: 156736
negative_passages.text: Prove that $\lim _{x \to \infty} x\sin x$ doesn't exist (using delta epsilon).
negative_passages.docid: 113765
negative_passages.text: $\lim_{x\to0} \frac{x-\sin x}{x-\tan x}$ without using L'Hopital
negative_passages.docid: 113086
negative_passages.text: Prove or disprove that $f(x) = \sin x/x$ is uniformly continuous over the interval $(0,1)$?
negative_passages.docid: 85531
negative_passages.text: Calculate $\lim_{x\to 0}\frac{1}{x^{\sin(x)}}$