query: What is the limit of $\lim\limits_{x→∞}\frac{\sin x}{x}$
positive_passages.docid: 122301
positive_passages.text: Evaluating and proving $\lim\limits_{x\to\infty}\frac{\sin x}x$
negative_passages.docid: 49460
negative_passages.text: Find the limit of the given function
negative_passages.docid: 29213
negative_passages.text: Limit of 1/x as x approaches infinity
negative_passages.docid: 103285
negative_passages.text: Limit of a periodic function
negative_passages.docid: 62137
negative_passages.text: question about the limit $\lim_{h\to0}\frac{\arcsin(x+h)-\arcsin(x)}{h}$
negative_passages.docid: 85249
negative_passages.text: Evaluating: $\lim\limits_{x\to0}\left(\frac{\sin x}{x}\right)^{{6}/{x^{2}}}$
negative_passages.docid: 156610
negative_passages.text: To prove the limit of $\frac{x^2+2\cos x-2}{x\sin^3 x}$ at zero is $1/12$
negative_passages.docid: 51231
negative_passages.text: Find the limit of $\frac{n^{x}}{(1 + x)^{n}}$
negative_passages.docid: 95397
negative_passages.text: Finding out the limit $\lim_{a \to \infty} \frac{f(a)\ln a}{a}$
negative_passages.docid: 84788
negative_passages.text: Find limit of $\lim_{x\to 0}\frac{\sin^{200}(x)}{x^{199}\sin(4x)}$, if it exists
negative_passages.docid: 33372
negative_passages.text: What is $\lim_{x\to\infty}\left(\sin{\frac 1x}+\cos{\frac 1x}\right)^x$?
negative_passages.docid: 83863
negative_passages.text: What is the limit of
negative_passages.docid: 79785
negative_passages.text: Determining the limit $\lim_{h\to0} \frac{\cos(x+h) - \cos(x)}{(x+h)^{1/2} - x^{1/2}}$
negative_passages.docid: 149102
negative_passages.text: Evaluating $\lim_{x \to 0} x\sin\left(\frac{1}{x}\right)$ or showing it does not exist
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: 150734
negative_passages.text: Solving $\lim\limits_{x\to0} \frac{x - \sin(x)}{x^2}$ without L'Hospital's Rule.
negative_passages.docid: 122990
negative_passages.text: How can I prove that $\lim\limits_{n\to\infty}\frac{n+\sin n}{n+1} = 1$