query: What is the value for $\lim_{x\to\infty} \frac{\sin x}{x}$?
positive_passages.docid: 122301
positive_passages.text: Evaluating and proving $\lim\limits_{x\to\infty}\frac{\sin x}x$
negative_passages.docid: 65975
negative_passages.text: Calculating $\lim_{n\to\infty}\sqrt{n}\sin(\sin...(\sin(x)..)$
negative_passages.docid: 51212
negative_passages.text: How do I solve $\lim\limits_{x\to\infty} \ \frac{\ln \ x}{x} = 0$?
negative_passages.docid: 85531
negative_passages.text: Calculate $\lim_{x\to 0}\frac{1}{x^{\sin(x)}}$
negative_passages.docid: 79299
negative_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: 142404
negative_passages.text: Evaluating limit making it $\frac{\infty}{\infty}$ and using L'Hopital Rule
negative_passages.docid: 17713
negative_passages.text: What's the value of $\sum\limits_{k=1}^{\infty}\frac{k^2}{k!}$?
negative_passages.docid: 139386
negative_passages.text: Limits of trigonometric functions: $\lim _{x\to \pi } \frac{\cos(x/2)}{\pi ^2-x^2}$
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: 125088
negative_passages.text: show that $ \lim(\sin(\frac{1}{x}))$ as $x$ approaches zero does not exist.
negative_passages.docid: 4224
negative_passages.text: Evaluate limit of an integral: $\lim_{x\to \infty }\frac{1}{x}\int _0^x\:\frac{dt}{2+\cos t}$
negative_passages.docid: 17069
negative_passages.text: Limit $\lim_{x\to \infty} \frac{\sqrt{x+1}+\sqrt{x+2}-\sqrt{4x+12}}{\sqrt{x+2}+\sqrt{x}-\sqrt{4x+12}}$
negative_passages.docid: 39798
negative_passages.text: Computing $\lim_{n \to \infty} \int_0^{n^2} e^{-x^2}n\sin\frac{x}{n}\,dx$?
negative_passages.docid: 33675
negative_passages.text: Find $\lim_{n\to \infty} \int_n^{n+1} {\sin x \over x} dx$
negative_passages.docid: 156231
negative_passages.text: Computing $\lim\limits_{n\to\infty} \int_{0}^{\infty}\frac{\sin(x/n)}{(1+x/n)^{n}}\, dx$
negative_passages.docid: 65266
negative_passages.text: A limit problem $\lim\limits_{x \to 0}\frac{x\sin(\sin x) - \sin^{2}x}{x^{6}}$
negative_passages.docid: 138169
negative_passages.text: Finding $\lim\limits_{n \to \infty }n\int_{0}^{1}\frac{x^{n}}{1+x+x^{n}}dx$