query: Find $\lim_{x\to-\infty} \frac{\ln(e^x+1)}{x}$
positive_passages.docid: 27511
positive_passages.text: Prove that $\lim_{x \to \infty} \frac{\log(1+e^x)}{x} = 1$
negative_passages.docid: 111929
negative_passages.text: Find the limit: $\lim_\limits{x\to 0}{\frac{\left(1+x\right)^{1/x}-e}{x}}$
negative_passages.docid: 123970
negative_passages.text: Find $L=\lim \limits_{n\to \infty}\sqrt[n]{x^n+y^n+z^n}$
negative_passages.docid: 142575
negative_passages.text: Find the value of : $\lim_{x\to\infty} \sqrt{x+\sqrt{x}}-\sqrt{x}$
negative_passages.docid: 109489
negative_passages.text: How to solve $ \lim_{n\to\infty} \frac {(n!)^\frac{1}{n}}{n} $?
negative_passages.docid: 3527
negative_passages.text: Finding $\lim_{n \to \infty} \prod_{r=1}^n (1+ \frac{1}{a_r})$
negative_passages.docid: 101743
negative_passages.text: Find the limit: $\lim \limits_{x \to 1} \left( {\frac{x}{{x - 1}} - \frac{1}{{\ln x}}} \right)$
negative_passages.docid: 33675
negative_passages.text: Find $\lim_{n\to \infty} \int_n^{n+1} {\sin x \over x} dx$
negative_passages.docid: 49128
negative_passages.text: How to prove $\lim\limits_{n \to \infty} (1+\frac1n)^n = e$?
negative_passages.docid: 30181
negative_passages.text: Proving that $\lim\limits_{x \to 0}\frac{e^x-1}{x} = 1$
negative_passages.docid: 93408
negative_passages.text: Trying to show that $\ln(x) = \lim_{n\to\infty} n(x^{1/n} -1)$
negative_passages.docid: 133244
negative_passages.text: Finding $\lim_{n \to \infty} n(\sqrt[n]{2} - 1)$
negative_passages.docid: 113913
negative_passages.text: using L'Hospital solve $\lim_{x \to \infty} x - x^{2}\ln(1 + \frac{1}{x})$
negative_passages.docid: 74286
negative_passages.text: Prove: $\lim_{n\to\infty} \frac{\sum^n_{k=1} \frac{1}{k}}{ \ln(n) } = 1$
negative_passages.docid: 73812
negative_passages.text: Does $\lim \limits_ {n\to \infty}\ \frac{n}{n+1}$ equal $1$?
negative_passages.docid: 17069
negative_passages.text: Limit $\lim_{x\to \infty} \frac{\sqrt{x+1}+\sqrt{x+2}-\sqrt{4x+12}}{\sqrt{x+2}+\sqrt{x}-\sqrt{4x+12}}$
negative_passages.docid: 41203
negative_passages.text: Finding $\lim\limits_{x \to \infty} (\sqrt{9x^2+x} - 3x)$