query: $\lim_{x \to 2} \frac{\cos{\left(\frac{\pi}{x}\right)}}{x-2}$ without using De L'Hospital
positive_passages.docid: 142114
positive_passages.text: Limit as $x\to 2$ of $\frac{\cos(\frac \pi x)}{x-2} $
negative_passages.docid: 111929
negative_passages.text: Find the limit: $\lim_\limits{x\to 0}{\frac{\left(1+x\right)^{1/x}-e}{x}}$
negative_passages.docid: 63617
negative_passages.text: Evaluating limit $\lim_{k\to \infty}\prod_{r=1}^k\cos{\left(\frac {x}{2^r}\right)}$
negative_passages.docid: 19056
negative_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: 117370
negative_passages.text: $\lim_{n\to\infty} \left(1+\frac{2}{n}\right)^{n^2} e^{-2n}$
negative_passages.docid: 139215
negative_passages.text: Find the value of $\lim_{x \to - \infty} \left( \sqrt{x^2 + 2x} - \sqrt{x^2 - 2x} \right)$
negative_passages.docid: 113765
negative_passages.text: $\lim_{x\to0} \frac{x-\sin x}{x-\tan x}$ without using L'Hopital
negative_passages.docid: 106867
negative_passages.text: Limit of $\cos(x)/x$ as $x$ approaches $0$
negative_passages.docid: 128456
negative_passages.text: Evaluating $\lim_{x\to0}\left(\frac{1+x2^x}{1+x3^x}\right)^\frac1{x^2}$
negative_passages.docid: 136450
negative_passages.text: Compute $\lim_{x \rightarrow +\infty} \frac{[\int^x_0 e^{y^{2}} dy]^2}{\int^x_0 e^{2y^{2}}dy}$
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: 22709
negative_passages.text: Show that $\lim_{x\to \frac{\pi}{2}} \frac{1}{\big(x-\frac{\pi}{2}\big)}+{\tan(x)}=0$.
negative_passages.docid: 51622
negative_passages.text: Evaluating $\lim\limits_{x\rightarrow0}\frac{e^{-1/x^2}}{x}$
negative_passages.docid: 118204
negative_passages.text: Finding limit of $\left(1 +\frac1x\right)^x$ without using L'Hôpital's rule.
negative_passages.docid: 30937
negative_passages.text: How do I find $\lim\limits_{x \to 0} x\cot(6x) $ without using L'hopitals rule?
negative_passages.docid: 30259
negative_passages.text: Evaluating the double limit $\lim_{m \to \infty} \lim_{n \to \infty} \cos^{2m}(n! \pi x)$
negative_passages.docid: 70086
negative_passages.text: Limit without l'Hopital or Taylor series: $\lim\limits_{x \to 0} \frac{x\cos x- \sin x}{x^3}$