query: limit for an oscillating function $\sin\frac{1}{x}$
positive_passages.docid: 79299
positive_passages.text: Strange behavior of $\lim_{x\to0}\frac{\sin\left(x\sin\left(\frac1x\right)\right)}{x\sin\left(\frac1x\right)}$
negative_passages.docid: 150734
negative_passages.text: Solving $\lim\limits_{x\to0} \frac{x - \sin(x)}{x^2}$ without L'Hospital's Rule.
negative_passages.docid: 128063
negative_passages.text: How to evaluate the limit $\lim_{x\to 0} \frac{1-\cos(4x)}{\sin^2(7x)}$
negative_passages.docid: 97571
negative_passages.text: Find the limit $ \lim_{n\to \infty} 2^{\frac{1}{n}}$
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: 106867
negative_passages.text: Limit of $\cos(x)/x$ as $x$ approaches $0$
negative_passages.docid: 37755
negative_passages.text: Limit $\lim_{x \to \infty}{\sin{\sqrt{x+1}}-\sin{\sqrt{x}}}$
negative_passages.docid: 113336
negative_passages.text: Limit of $(\frac{1}{n^2})^{(\frac{1}{n})}$
negative_passages.docid: 155979
negative_passages.text: $\lim_{x\to 0} \frac{\sin x - x}{x^2}$ without L'Hospital or Taylor
negative_passages.docid: 28413
negative_passages.text: Limit of a continuous function
negative_passages.docid: 152262
negative_passages.text: Limit of function of hyperbolic
negative_passages.docid: 135565
negative_passages.text: Limit of $\frac{1}{x^2}-\frac{1}{\sin^2(x)}$ as $x$ approaches $0$
negative_passages.docid: 142114
negative_passages.text: Limit as $x\to 2$ of $\frac{\cos(\frac \pi x)}{x-2} $
negative_passages.docid: 45728
negative_passages.text: Proving a limit of a trigonometric function: $\lim_{x \to 2/\pi}\lfloor \sin \frac{1}{x} \rfloor=0$
negative_passages.docid: 43829
negative_passages.text: Limit of $h_n(x)=x^{1+\frac{1}{2n-1}}$
negative_passages.docid: 151977
negative_passages.text: Dirac delta function as a limit of sinc function
negative_passages.docid: 17069
negative_passages.text: Limit $\lim_{x\to \infty} \frac{\sqrt{x+1}+\sqrt{x+2}-\sqrt{4x+12}}{\sqrt{x+2}+\sqrt{x}-\sqrt{4x+12}}$