query: Calculate $\lim\limits_{ x\to \infty} \frac{\ln(x)}{x^a}$ where $ a > 0 $
positive_passages.docid: 1840
positive_passages.text: How can I prove that $\log^k(n) = O(n^\epsilon)$?
negative_passages.docid: 118893
negative_passages.text: Calculate the limit: $\lim_{x\to\infty} \sqrt[x]{3^x+7^x}$
negative_passages.docid: 113289
negative_passages.text: finding the limit $\lim\limits_{x \to \infty }(\frac{1}{e}(1+\frac{1}{x})^x)^x$
negative_passages.docid: 82837
negative_passages.text: Calculating limit of function
negative_passages.docid: 9746
negative_passages.text: Determine the following limit as x approaches 0: $\frac{\ln(1+x)}x$
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: 135159
negative_passages.text: Limits using L'Hopital's rule $\lim_{x\to0^+} (x^{x^x-1})$
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: 144719
negative_passages.text: How to find $\lim\limits_{n\rightarrow \infty}\frac{(\log n)^p}{n}$
negative_passages.docid: 48985
negative_passages.text: Calculating $\lim_{x\to+\infty}(\sqrt{x^2-3x}-x)$
negative_passages.docid: 96011
negative_passages.text: Find $\lim_{n\to\infty}\frac{a^n}{n!}$
negative_passages.docid: 17090
negative_passages.text: Compute $\lim_\limits{n\to\infty}a_n$ where $a_{n+2}=\sqrt{a_n.a_{n+1}}$
negative_passages.docid: 32853
negative_passages.text: Computing $\lim_{A\to\infty} \frac{1}{A} \int\limits_1^A \! A^{\frac{1}{x}} \, \mathrm{d}x.$
negative_passages.docid: 37394
negative_passages.text: How to find $\lim\limits_{n\to\infty} n·(\sqrt[n]{a}-1)$?
negative_passages.docid: 147514
negative_passages.text: How to calculate $\lim \limits_{n \to \infty}(1 +\frac{a}{n})^n$?
negative_passages.docid: 18079
negative_passages.text: Evaluating $\lim\limits_{x\to \infty}\sqrt[6]{x^{6}+x^{5}}-\sqrt[6]{x^{6}-x^{5}}$
negative_passages.docid: 83318
negative_passages.text: How to compute the limit $\lim_{n \to \infty} \sqrt[n]{a_1^n + \cdots + a_m^n}$?