query: Solve limit without L'Hopital: $\lim_{x \to 0} \frac{2 \sin x-\sin 2x}{x-\sin x}$
positive_passages.docid: 19056
positive_passages.text: Find the limit of $(2\sin x-\sin 2x)/(x-\sin x)$ as $x\to 0$ without L'Hôpital's rule
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: 86634
negative_passages.text: How to find $ \lim_{(x,y)\to(0,0)} \frac{\sin^2 (x-y)}{|x|+|y|} $?
negative_passages.docid: 106742
negative_passages.text: Evaluating $ \lim_{x \rightarrow 0}\left (\frac{\sin(x)}{x}\right)^\frac{1}{x^2}$
negative_passages.docid: 85531
negative_passages.text: Calculate $\lim_{x\to 0}\frac{1}{x^{\sin(x)}}$
negative_passages.docid: 56085
negative_passages.text: Calculate the limit : $\lim_{x \to 0}\frac{x-\sin{x}}{x^3}$ WITHOUT using L'Hopital's rule
negative_passages.docid: 79618
negative_passages.text: Find the limit without use of L'Hôpital or Taylor series: $\lim \limits_{x\rightarrow 0} \left(\frac{1}{x^2}-\frac{1}{\sin^2 x}\right)$
negative_passages.docid: 28161
negative_passages.text: Solve $\lim_{x\to 0} \frac{\sin x-x}{x^3}$
negative_passages.docid: 23489
negative_passages.text: Limit of $\left(1+\frac{a}{x}\right)^x$ with and without L'Hôpital's rule
negative_passages.docid: 95991
negative_passages.text: How to solve $\lim_{x \rightarrow 0} {\frac{(1+x)^a-1}{x}}$?
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: 26408
negative_passages.text: Evaluate a limit (probably involving L'Hôpital rule)
negative_passages.docid: 118204
negative_passages.text: Finding limit of $\left(1 +\frac1x\right)^x$ without using L'Hôpital's rule.
negative_passages.docid: 101743
negative_passages.text: Find the limit: $\lim \limits_{x \to 1} \left( {\frac{x}{{x - 1}} - \frac{1}{{\ln x}}} \right)$
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: 100893
negative_passages.text: Determine $\lim_{x \to 0}{\frac{x-\sin{x}}{x^3}}=\frac{1}{6}$, without L'Hospital or Taylor
negative_passages.docid: 65266
negative_passages.text: A limit problem $\lim\limits_{x \to 0}\frac{x\sin(\sin x) - \sin^{2}x}{x^{6}}$