query: Computing $ \lim_{x \to 0} \left( \frac {1}{x} - \frac {1}{\sin x } \right) $
positive_passages.docid: 64001
positive_passages.text: What is the result of $\lim\limits_{x \to 0}(1/x - 1/\sin x)$?
negative_passages.docid: 13104
negative_passages.text: What is $\lim_{x \to \infty} \frac{\sin x}{\sin x}?$
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: 146640
negative_passages.text: Computing $\lim_{(x,y)\to (0,0)}\frac{x+y}{\sqrt{x^2+y^2}}$
negative_passages.docid: 150981
negative_passages.text: Why doesn't using the approximation $\sin x\approx x$ near $0$ work for computing this limit?
negative_passages.docid: 569
negative_passages.text: How do I determine $\lim_{x\to\infty} \left[x - x^{2} \log\left(1 + 1/x\right)\right]$?
negative_passages.docid: 7309
negative_passages.text: Why $\lim\limits_{n\to \infty}\left(1+\frac{1}{n}\right)^n$ doesn't evaluate to 1?
negative_passages.docid: 156231
negative_passages.text: Computing $\lim\limits_{n\to\infty} \int_{0}^{\infty}\frac{\sin(x/n)}{(1+x/n)^{n}}\, dx$
negative_passages.docid: 27717
negative_passages.text: Compute $\lim_{x\to\infty}x\;\left[\left(1+\frac{1}{x}\right)^x-e\right]$
negative_passages.docid: 96112
negative_passages.text: Differentiating $ \left( 1 - \frac {1}{x} \right)^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: 113765
negative_passages.text: $\lim_{x\to0} \frac{x-\sin x}{x-\tan x}$ without using L'Hopital
negative_passages.docid: 68136
negative_passages.text: $\lim\limits_{x\to 0} \frac{\tan x - \sin x}{x^3}$?
negative_passages.docid: 40463
negative_passages.text: Evaluating $\lim _{x\to 1}\left(\frac{\sqrt[3]{x}-1}{2\sqrt{x}-2}\right)$
negative_passages.docid: 9746
negative_passages.text: Determine the following limit as x approaches 0: $\frac{\ln(1+x)}x$
negative_passages.docid: 28161
negative_passages.text: Solve $\lim_{x\to 0} \frac{\sin x-x}{x^3}$
negative_passages.docid: 69502
negative_passages.text: How to evaluate $\lim\limits_{x\to 0+}\frac 1x \left(\frac 1{\tan^{-1}x}-\frac 1x\right)$?