query: L'Hopital rule to solve $ \lim\limits_{x\to 0} \left(\frac{\sin x}{x}\right)^{\frac{1}{x^{2}}} $
positive_passages.docid: 117542
positive_passages.text: Finding the limit $\displaystyle\lim_{x\to 0+} \left(\frac{\sin x}x\right)^{1/{x^2}}$
negative_passages.docid: 95962
negative_passages.text: proving a theorem from limit using Hopital rule
negative_passages.docid: 7819
negative_passages.text: Calculate: $ \lim_{x \to 0 } = x \cdot \sin(\frac{1}{x}) $
negative_passages.docid: 90431
negative_passages.text: Compute $\lim_{x\to 0} \frac{e^{-1/x^2}}{x}$ without using L'Hopital?
negative_passages.docid: 70086
negative_passages.text: Limit without l'Hopital or Taylor series: $\lim\limits_{x \to 0} \frac{x\cos x- \sin x}{x^3}$
negative_passages.docid: 102408
negative_passages.text: Evaluate the limit $\lim_{x \to 0}{\frac{\sqrt{1+x\sin{x}}-\sqrt{\cos{2x}}}{\tan^{2}{\frac{x}{2}}}}$
negative_passages.docid: 65213
negative_passages.text: How to find $\lim\limits_{x\to0}\frac{e^x-1-x}{x^2}$ without using l'Hopital's rule nor any series expansion?
negative_passages.docid: 85249
negative_passages.text: Evaluating: $\lim\limits_{x\to0}\left(\frac{\sin x}{x}\right)^{{6}/{x^{2}}}$
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: 74919
negative_passages.text: Finding limit of function $\lim_{x\to 0}\left(\frac{(1+x)^\frac1x}{e}\right)^\frac1x$
negative_passages.docid: 41366
negative_passages.text: Compute $\lim\limits_{n\to\infty} \left(1+\frac{1}{n}\right)\left(1+\frac{2}{n}\right)^{{1}/{2}}\cdots\left(1+\frac{n}{n}\right)^{{1}/{n}}$
negative_passages.docid: 41419
negative_passages.text: Solution of limit $\lim\limits_{x\to 0} \frac {e^{-1/x^2}}{x} $
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: 23217
negative_passages.text: About $\lim \left(1+\frac {x}{n}\right)^n$
negative_passages.docid: 144329
negative_passages.text: Help solving a limit in two parts $\lim_{t\to 0}\left(\frac{1}{t\sqrt{1+t}}-\frac{1}{t}\right)$
negative_passages.docid: 113913
negative_passages.text: using L'Hospital solve $\lim_{x \to \infty} x - x^{2}\ln(1 + \frac{1}{x})$
negative_passages.docid: 33372
negative_passages.text: What is $\lim_{x\to\infty}\left(\sin{\frac 1x}+\cos{\frac 1x}\right)^x$?