query: How is $\frac{\sin(x)}{x} = 1$ at $x = 0$
positive_passages.docid: 17029
positive_passages.text: How to prove that $\lim\limits_{x\to0}\frac{\sin x}x=1$?
negative_passages.docid: 55577
negative_passages.text: Why is $\frac{1}{\infty } \approx 0 $ and $ \frac{1}{0} = {\infty}$?
negative_passages.docid: 64941
negative_passages.text: Why is $1 - \frac{1}{1 - \frac{1}{1 - \ldots}}$ not real?
negative_passages.docid: 82170
negative_passages.text: Solve $x = \frac{1}{2}\tan(x)$
negative_passages.docid: 13104
negative_passages.text: What is $\lim_{x \to \infty} \frac{\sin x}{\sin x}?$
negative_passages.docid: 28161
negative_passages.text: Solve $\lim_{x\to 0} \frac{\sin x-x}{x^3}$
negative_passages.docid: 41659
negative_passages.text: Limit as $x\to 0$ of $x\sin(1/x)$
negative_passages.docid: 80060
negative_passages.text: Is $\frac{1}{\infty}$  equal zero?
negative_passages.docid: 144811
negative_passages.text: Calculate $\int_0^{2\pi} \frac{1}{2+\sin(x)} \ dx$
negative_passages.docid: 13533
negative_passages.text: Proof that the limit of $\frac{1}{x}$ as $x$ approaches $0$ does not exist
negative_passages.docid: 112898
negative_passages.text: Derivative of sin(x)/x at $0$ by definition of derivative
negative_passages.docid: 123899
negative_passages.text: $\int_0^{+\infty}\frac{\sin(x)}{x^\alpha}dx=\frac{\Gamma(\alpha/2)\Gamma(1-\alpha/2)}{2\Gamma(\alpha)}$
negative_passages.docid: 27969
negative_passages.text: Why does $\frac{1}{x} < 4$ have two answers?
negative_passages.docid: 131310
negative_passages.text: Evaluating $\dfrac{1}{\sin(2x)} + \dfrac{1}{\sin(4x)} + \dfrac{1}{\sin(8x)} + \dfrac{1}{\sin(16x)}$
negative_passages.docid: 87055
negative_passages.text: How to prove $\frac{x}{1+x^2}0$?
negative_passages.docid: 150601
negative_passages.text: The limit of $\sin(1/x)$ as $x\to 0$ does not exists
negative_passages.docid: 10289
negative_passages.text: Need help in proving that $\frac{\sin\theta - \cos\theta + 1}{\sin\theta + \cos\theta - 1} = \frac 1{\sec\theta - \tan\theta}$