query: How to evaluate $\lim_{x\to0} \frac{(1+x)^{\frac1x} - e}{x}$ with Taylor series
positive_passages.docid: 50300
positive_passages.text: How to solve this limit: $\lim\limits_{x\to0}\frac{(1+x)^{1/x}-e}x$?
negative_passages.docid: 11382
negative_passages.text: Limit $\lim\limits_{x\to0}\frac1{\ln(x+1)}-\frac1x$
negative_passages.docid: 3424
negative_passages.text: Use taylor series to arrive at the expression f'(x)=1/h[-3*f(x)/2+2f(x+h)-f(x+2h)/2]
negative_passages.docid: 109059
negative_passages.text: Evaluate $\lim\limits_{n\to \infty}\frac{1}{n+1}+\frac{1}{n+2}+\cdots+\frac{1}{6n}$
negative_passages.docid: 105860
negative_passages.text: Evaluate the limit of $(n+1)\int_0^1x^n\ln(1+x)\,dx$ when $n\to\infty$
negative_passages.docid: 44668
negative_passages.text: Limit of $x\left(\left(1 + \frac{1}{x}\right)^x - e\right)$ when $x\to\infty$
negative_passages.docid: 142404
negative_passages.text: Evaluating limit making it $\frac{\infty}{\infty}$ and using L'Hopital Rule
negative_passages.docid: 154506
negative_passages.text: Evaluating $\lim_{n\rightarrow\infty} (\frac{(1+\frac{1}{n})^n}{e})^n$
negative_passages.docid: 68550
negative_passages.text: What is the radius of convergence of the Taylor series of $\frac{2\tan x}{1+4x^2}$ around $x=0?$
negative_passages.docid: 151788
negative_passages.text: nth derivative of $\frac{e^x−1}{x}$ (both taylor series and finite sum)
negative_passages.docid: 71743
negative_passages.text: $\lim (1+\frac{1}{n+1})^n = e$
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: 79785
negative_passages.text: Determining the limit $\lim_{h\to0} \frac{\cos(x+h) - \cos(x)}{(x+h)^{1/2} - x^{1/2}}$
negative_passages.docid: 30181
negative_passages.text: Proving that $\lim\limits_{x \to 0}\frac{e^x-1}{x} = 1$
negative_passages.docid: 119243
negative_passages.text: Taylor Series Expansion of $\frac{1}{\sin 2x}$ and $\frac{1}{1-e^{-x}}$
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: 54775
negative_passages.text: Find $\lim_{n \to \infty} n[(1+\frac{1}{n})^n - e]$