query: Find $\lim_{x\to 0} \frac{(1+x)^{1/x} - e}{x}$
positive_passages.docid: 19263
positive_passages.text: Limit as $x\to 0$ of $\frac{(1+x)^{1/x}-e}{x}$
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: 54775
negative_passages.text: Find $\lim_{n \to \infty} n[(1+\frac{1}{n})^n - e]$
negative_passages.docid: 56671
negative_passages.text: Find the limit $ \lim_{x \to \infty} \frac{e^{x}}{(1+\frac{1}{x})^{x^{2}}} $
negative_passages.docid: 138169
negative_passages.text: Finding $\lim\limits_{n \to \infty }n\int_{0}^{1}\frac{x^{n}}{1+x+x^{n}}dx$
negative_passages.docid: 26211
negative_passages.text: Computing $\lim_{x \to \infty} x \biggl[ \frac{1}{e} - \left( \frac{x}{x+1} \right)^x \biggr]$
negative_passages.docid: 114862
negative_passages.text: Find the limit $\displaystyle \lim_{x \to 0^+} (\sin x)^\frac1{\ln x}$
negative_passages.docid: 66526
negative_passages.text: Find the limit of: $\lim_{n\to\infty} \frac{1}{\sqrt[n+1]{(n+1)!} - \sqrt[n]{(n)!}}$
negative_passages.docid: 101716
negative_passages.text: Find this limit: $ \lim_{n \to \infty}{(e^{\frac{1}{n}} - \frac{2}{n})^n}$
negative_passages.docid: 54830
negative_passages.text: Find the limit $\lim\limits_{x\to\infty} f(x)= \lim\limits_{x \to \infty} \left(\frac{x}{x+1}\right)^x$
negative_passages.docid: 35260
negative_passages.text: Evaluate the limit $\displaystyle\lim_{x \to 0}\frac{(e-\left(1 + x\right)^{1/x})}{\tan x}$.
negative_passages.docid: 98392
negative_passages.text: Value of the limit $\lim_{x \to 0} \frac{\sin(\frac{1}{x})}{\sin(\frac{1}{x})}$
negative_passages.docid: 158591
negative_passages.text: I want to calculate the limit of: $\lim_{x \to 0} \left(\frac{2^x+8^x}{2} \right)^\frac{1}{x} $
negative_passages.docid: 145913
negative_passages.text: Find $\lim_{x\rightarrow 0} \frac{\cos x - 1}{x}$
negative_passages.docid: 41515
negative_passages.text: fine the limit : $\lim_{ n \to \infty }\frac{1}{n}\int_{0}^{n}{ \frac{x\ln(1+\frac{x}{n})}{1+x}}=?$
negative_passages.docid: 88782
negative_passages.text: Finding the limit of $x_1=0 , x_{n+1}=\frac{1}{1+x_n}$
negative_passages.docid: 27511
negative_passages.text: Prove that $\lim_{x \to \infty} \frac{\log(1+e^x)}{x} = 1$