query: Limit of $\lim\limits_{x \to \infty}\frac{1}{\cosh(x)}+\log\left(\frac{\cosh(x)}{1+\cosh(x)}\right)$ without l'hopital
positive_passages.docid: 152262
positive_passages.text: Limit of function of hyperbolic
negative_passages.docid: 56265
negative_passages.text: limit $\lim\limits_{n\to\infty}\left(\sum\limits_{i=1}^{n}\frac{1}{\sqrt{i}} - 2\sqrt{n}\right)$
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: 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: 156546
negative_passages.text: Evaluate the limit $\lim_{n\rightarrow \infty}\frac{1}{\sqrt{n}}\left(1+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+\ldots+\frac{1}{\sqrt{n}}\right)$
negative_passages.docid: 82831
negative_passages.text: Evaluating the limit $\lim_{n\to\infty} \left[ \frac{n}{n^2+1}+ \frac{n}{n^2+2^2} + \ldots + \frac{n}{n^2+n^2} \right]$
negative_passages.docid: 94910
negative_passages.text: How does one show that $\lim_{x\rightarrow\infty}\left(1+\frac{1}{x}\right)^x$ converges?
negative_passages.docid: 113537
negative_passages.text: Limit $\lim_{n\to\infty}\left(1-\frac{1}{3}\right)^2\left(1-\frac{1}{6}\right)^2\cdots\left(1-\frac{1}{\frac{n(n+1)}{2}}\right)^2$
negative_passages.docid: 132988
negative_passages.text: $ \lim_{n \to \infty} \left(\frac 1{n^2+1}+\frac 2{n^2+2}+\frac 3{n^2+3}+\cdots +\frac n{n^2+n}\right)$
negative_passages.docid: 120493
negative_passages.text: L'hopitals rule with limits
negative_passages.docid: 73865
negative_passages.text: Find $\lim_{n\to\infty}n\left(\sum_{i=1}^{n}\dfrac{1}{(n+i)^2}\right)$
negative_passages.docid: 63165
negative_passages.text: Is this limit correct: $\lim_{x \to+\infty} \frac{\log_{2}(x-1)}{x} = 0$?
negative_passages.docid: 136738
negative_passages.text: Does the limit $\lim _{x\to 0} \frac 1x \int_0^x \left|\cos \frac 1t \right| dt$ exists?
negative_passages.docid: 91523
negative_passages.text: Prove this limit as $x\to\infty$
negative_passages.docid: 27717
negative_passages.text: Compute $\lim_{x\to\infty}x\;\left[\left(1+\frac{1}{x}\right)^x-e\right]$
negative_passages.docid: 16739
negative_passages.text: The Limit of $x\left(\sqrt[x]{a}-1\right)$ as $x\to\infty$.
negative_passages.docid: 76990
negative_passages.text: Find $\lim_{x \to - \infty} \left(\frac{4^{x+2}- 2\cdot3^{-x}}{4^{-x}+2\cdot3^{x+1}}\right)$