query: Finding limit of two quotients: $\lim_{t \to 0} \left(\frac{1}{t\sqrt{1+t}}- \frac 1 t\right)$
positive_passages.docid: 144329
positive_passages.text: Help solving a limit in two parts $\lim_{t\to 0}\left(\frac{1}{t\sqrt{1+t}}-\frac{1}{t}\right)$
negative_passages.docid: 128218
negative_passages.text: If $\lim \limits_{x \to a}\left(f(x)+\frac{1}{f(x)}\right)=2,$ then $\lim \limits_{x \to a}f(x)=1$
negative_passages.docid: 40463
negative_passages.text: Evaluating $\lim _{x\to 1}\left(\frac{\sqrt[3]{x}-1}{2\sqrt{x}-2}\right)$
negative_passages.docid: 23489
negative_passages.text: Limit of $\left(1+\frac{a}{x}\right)^x$ with and without L'Hôpital's rule
negative_passages.docid: 106281
negative_passages.text: Prove $\lim\limits_{n\to \infty}\frac{1}{\sqrt n}\left|\sum\limits_{k=1}^n (-1)^k\sqrt k\right|= \frac{1}{2}$
negative_passages.docid: 95991
negative_passages.text: How to solve $\lim_{x \rightarrow 0} {\frac{(1+x)^a-1}{x}}$?
negative_passages.docid: 72842
negative_passages.text: Evaluation of the limit $\lim\limits_{n \to \infty } \frac1{\sqrt n}\left(1 + \frac1{\sqrt 2 }+\frac1{\sqrt 3 }+\cdots+\frac1{\sqrt n } \right)$
negative_passages.docid: 158591
negative_passages.text: I want to calculate the limit of: $\lim_{x \to 0} \left(\frac{2^x+8^x}{2} \right)^\frac{1}{x} $
negative_passages.docid: 11382
negative_passages.text: Limit $\lim\limits_{x\to0}\frac1{\ln(x+1)}-\frac1x$
negative_passages.docid: 125538
negative_passages.text: limit of $n^{\frac{1}{\sqrt{n}}}$
negative_passages.docid: 117542
negative_passages.text: Finding the limit $\displaystyle\lim_{x\to 0+} \left(\frac{\sin x}x\right)^{1/{x^2}}$
negative_passages.docid: 79684
negative_passages.text: Finding $\lim \limits_{x \to 0} \frac{1 - \cos x}{x}$, given $\lim \limits_{x \to 0} \frac{\sin x}{x} = 1$
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: 76990
negative_passages.text: Find $\lim_{x \to - \infty} \left(\frac{4^{x+2}- 2\cdot3^{-x}}{4^{-x}+2\cdot3^{x+1}}\right)$
negative_passages.docid: 155353
negative_passages.text: Find the limit of $ a_n =\left(1+\frac{1^2}{n^2}\right)^1\left(1+\frac{2^2}{n^2}\right)^2\cdots \left(1+\frac{n^2}{n^2}\right)^n$
negative_passages.docid: 88925
negative_passages.text: How find this limit $\lim\limits_{x\to 0^{+}}\frac{\sin{(\tan{x})}-\tan{(\sin{x})}}{x^7}$
negative_passages.docid: 156141
negative_passages.text: Limit of $\left(1-\frac{1}{n^2}\right)^n$