query: Another method for limit of $[e-(1+x)^{1/x}]/x$ as $x$ approaches zero
positive_passages.docid: 19263
positive_passages.text: Limit as $x\to 0$ of $\frac{(1+x)^{1/x}-e}{x}$
negative_passages.docid: 89251
negative_passages.text: Limit $\lim\limits_{x\to0}{\frac{\ln{(e+x)}-e^x}{\cos^2{x} -e^x}}$
negative_passages.docid: 144273
negative_passages.text: Find $\lim_{n\to\infty} \frac{1}{n} \int_0^\infty f(x) e^{-a_n x} dx$
negative_passages.docid: 51622
negative_passages.text: Evaluating $\lim\limits_{x\rightarrow0}\frac{e^{-1/x^2}}{x}$
negative_passages.docid: 135731
negative_passages.text: Is there a way to show that $e^x=\lim_{n\to \infty }\left(1+\frac{x}{n}\right)^n$?
negative_passages.docid: 50300
negative_passages.text: How to solve this limit: $\lim\limits_{x\to0}\frac{(1+x)^{1/x}-e}x$?
negative_passages.docid: 60831
negative_passages.text: Need hint for $\lim_{x\to 0} \frac{(x+1)^\frac{1}{x}-e}{x}$
negative_passages.docid: 114675
negative_passages.text: Evaluating $\lim\limits_{x\to 0}(1+x)^{1/x}$?
negative_passages.docid: 26408
negative_passages.text: Evaluate a limit (probably involving L'Hôpital rule)
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: 147514
negative_passages.text: How to calculate $\lim \limits_{n \to \infty}(1 +\frac{a}{n})^n$?
negative_passages.docid: 109489
negative_passages.text: How to solve $ \lim_{n\to\infty} \frac {(n!)^\frac{1}{n}}{n} $?
negative_passages.docid: 155539
negative_passages.text: Evaluating the limit $\lim_{x \to 0+}\left(\frac{1}{x}-\frac{1}{\arctan(x)}\right)$
negative_passages.docid: 23489
negative_passages.text: Limit of $\left(1+\frac{a}{x}\right)^x$ with and without L'Hôpital's rule
negative_passages.docid: 71743
negative_passages.text: $\lim (1+\frac{1}{n+1})^n = e$
negative_passages.docid: 29213
negative_passages.text: Limit of 1/x as x approaches infinity
negative_passages.docid: 12378
negative_passages.text: Find the limit $\displaystyle\lim_{n\rightarrow\infty}{(1+1/n)^{n^2}e^{-n}}$?