query: Limits and exponential: $\lim\limits_{x \to\infty} (x-x^2 \ln(1+1/x))$
positive_passages.docid: 569
positive_passages.text: How do I determine $\lim_{x\to\infty} \left[x - x^{2} \log\left(1 + 1/x\right)\right]$?
negative_passages.docid: 56048
negative_passages.text: Limit at infinity of $x^{1/x}$
negative_passages.docid: 140574
negative_passages.text: Find $\lim_{n\to \infty} \int_0^1 nx^n e^{x^2} dx$
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: 97747
negative_passages.text: Limit of $\lim\limits_{n\to\infty} (1 + \frac{x_n}{n})^n$
negative_passages.docid: 53109
negative_passages.text: Why is this limit $\lim_{n \to \infty}(1 + \frac{1}{n})^n$ equal to $e$?
negative_passages.docid: 17329
negative_passages.text: How do I find this limit: $\lim_{n\to\infty} \left[ n-{n\over e}\left(1+{1\over n}\right)^n \right]$?
negative_passages.docid: 114924
negative_passages.text: What is $ \lim_{n\to\infty}\frac{1}{e^n}\Bigl(1+\frac1n\Bigr)^{n^2}$?
negative_passages.docid: 106527
negative_passages.text: Limit of $(\cos1/n)^{n^2}$ when $n\to\infty$
negative_passages.docid: 134787
negative_passages.text: How to prove $\lim \limits_{n\to\infty}(n+1)\int_{0}^{1}x^nf(x)dx=f(1)$
negative_passages.docid: 13486
negative_passages.text: Show $\lim \limits_{n \to \infty} \frac{a_{n+1}}{a_n} = \|f\|_{\infty}$ for $f \in L^{\infty}$
negative_passages.docid: 144422
negative_passages.text: How to prove that $\lim\limits_{x\to\infty} f(x)/x=L$
negative_passages.docid: 146529
negative_passages.text: Finding the limit $ \lim_{x\to a^+} \frac{\cos(x)\ln(x-a)}{\ln(e^x-e^a)} $
negative_passages.docid: 138930
negative_passages.text: What does $\lim\limits_{x \to \infty} f(x) = 1$ say about $\lim\limits_{x \to \infty} f'(x)$?
negative_passages.docid: 19263
negative_passages.text: Limit as $x\to 0$ of $\frac{(1+x)^{1/x}-e}{x}$
negative_passages.docid: 43703
negative_passages.text: Find $\lim _{x\to \infty }\left(x\left(\ln\left(x+1\right)-\ln x\right)\right) $
negative_passages.docid: 968
negative_passages.text: $\lim_{x\to0^{+}} x \ln x$ without l'Hopital's rule