query: The limit of $((1+x)^{1/x}-e)/x\;$ as $\;x$ tends to $ 0$
positive_passages.docid: 19263
positive_passages.text: Limit as $x\to 0$ of $\frac{(1+x)^{1/x}-e}{x}$
negative_passages.docid: 30181
negative_passages.text: Proving that $\lim\limits_{x \to 0}\frac{e^x-1}{x} = 1$
negative_passages.docid: 32744
negative_passages.text: A clarification in a limit
negative_passages.docid: 119984
negative_passages.text: Limit of $0/x$ as x goes to 0
negative_passages.docid: 155188
negative_passages.text: How do I prove this limit does not exist: $\lim_{x\rightarrow 0} \frac{e^{1/x} - 1}{e^{1/x} + 1} $
negative_passages.docid: 150601
negative_passages.text: The limit of $\sin(1/x)$ as $x\to 0$ does not exists
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: 13533
negative_passages.text: Proof that the limit of $\frac{1}{x}$ as $x$ approaches $0$ does not exist
negative_passages.docid: 51231
negative_passages.text: Find the limit of $\frac{n^{x}}{(1 + x)^{n}}$
negative_passages.docid: 29213
negative_passages.text: Limit of 1/x as x approaches infinity
negative_passages.docid: 125497
negative_passages.text: Evaluating $\lim_{n \to \infty} n\left(1-\frac{1}{e}\left(1+\frac{1}{n}\right)^{n} \right)$
negative_passages.docid: 104229
negative_passages.text: Show that $\lim\limits_{y\downarrow 0} y\mathbb{E}[\frac{1}{X};X>y]=0$.
negative_passages.docid: 104269
negative_passages.text: Why does $\lim\limits_{t\to-\infty}te^t=0$?
negative_passages.docid: 9746
negative_passages.text: Determine the following limit as x approaches 0: $\frac{\ln(1+x)}x$
negative_passages.docid: 43538
negative_passages.text: Show $\lim_{n \to \infty} n^{-1} E \left( \frac{1}{X}1_{[X>n^{-1}]} \right) =0$
negative_passages.docid: 71743
negative_passages.text: $\lim (1+\frac{1}{n+1})^n = e$
negative_passages.docid: 105860
negative_passages.text: Evaluate the limit of $(n+1)\int_0^1x^n\ln(1+x)\,dx$ when $n\to\infty$