query: Find the limit $\lim_{x\to 0}\frac{\sqrt[5]{1+\sin x}-1}{\ln(1+\tan x)}$
positive_passages.docid: 156448
positive_passages.text: Evaluate the limit without using the L'Hôpital's rule
negative_passages.docid: 19791
negative_passages.text: Calculating $\lim_{x\to0} \left\lfloor\frac{x^2}{\sin x \tan x}\right\rfloor$
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: 20773
negative_passages.text: Find $\lim\limits_{n \to \infty} \frac{\sqrt 1 + \sqrt 2 + \dots + \sqrt{n}}{n\sqrt{n}}$.
negative_passages.docid: 18156
negative_passages.text: Find $\lim_{x\to \infty} \ln(x+1)/(\ln(x))$
negative_passages.docid: 31174
negative_passages.text: Find the limit if it exists of $S_{n+1} = \frac{1}{2}(S_n +\frac{A}{S_n})$
negative_passages.docid: 80314
negative_passages.text: Finding $\lim\limits_{x\to 0}\frac{\sin{3x}}{x}$
negative_passages.docid: 6304
negative_passages.text: Evaluate $\lim_{(x,y) \to (0,0), x+y \neq 0}{\frac{\ln(1-x-y)}{x+y} } $
negative_passages.docid: 45728
negative_passages.text: Proving a limit of a trigonometric function: $\lim_{x \to 2/\pi}\lfloor \sin \frac{1}{x} \rfloor=0$
negative_passages.docid: 113289
negative_passages.text: finding the limit $\lim\limits_{x \to \infty }(\frac{1}{e}(1+\frac{1}{x})^x)^x$
negative_passages.docid: 113765
negative_passages.text: $\lim_{x\to0} \frac{x-\sin x}{x-\tan x}$ without using L'Hopital
negative_passages.docid: 17029
negative_passages.text: How to prove that $\lim\limits_{x\to0}\frac{\sin x}x=1$?
negative_passages.docid: 117542
negative_passages.text: Finding the limit $\displaystyle\lim_{x\to 0+} \left(\frac{\sin x}x\right)^{1/{x^2}}$
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: 74919
negative_passages.text: Finding limit of function $\lim_{x\to 0}\left(\frac{(1+x)^\frac1x}{e}\right)^\frac1x$
negative_passages.docid: 99975
negative_passages.text: Find the Limit (n to infinity)
negative_passages.docid: 136810
negative_passages.text: Evaluate $\lim_{x \to 0} \frac{\sqrt{1 + \tan x} - \sqrt{1 + \sin x}}{x^3}$