query: limit $\lim_{n\rightarrow \infty}\left(\int_0^1f^n(x)dx\right)^{\frac{1}{n}}=M$
positive_passages.docid: 45988
positive_passages.text: limit of Holder norms: $\sup\limits_{x\in [a,b]} f(x) = \lim\limits_{n\rightarrow\infty} \left(\int_a^b (f(x))^n \;dx\right)^{\frac{1}{n}}$
negative_passages.docid: 107953
negative_passages.text: Limit of the sequence $\lim_{n\rightarrow\infty}\sqrt[n]n$
negative_passages.docid: 106742
negative_passages.text: Evaluating $ \lim_{x \rightarrow 0}\left (\frac{\sin(x)}{x}\right)^\frac{1}{x^2}$
negative_passages.docid: 21380
negative_passages.text: Proof for $e^z = \lim \limits_{x \rightarrow \infty} \left( 1 + \frac{z}{x} \right)^x$
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: 58334
negative_passages.text: How to find $\lim_{n \rightarrow +\infty } \left(\sqrt[m]{\prod_{i=1}^{m}(n+{a}_{i})}-n\right)$?
negative_passages.docid: 40227
negative_passages.text: Compute $\lim\limits_{n\to\infty}n^2\left(\left(1+\frac1{n+1}\right)^{n+1}-\left(1+\frac1n\right)^n\right)$
negative_passages.docid: 156141
negative_passages.text: Limit of $\left(1-\frac{1}{n^2}\right)^n$
negative_passages.docid: 11622
negative_passages.text: Find $\lim _{n\to \infty }\left(\frac{1}{n^2+1}+\frac{1}{n^2+2}+...+\frac{1}{n^2+n}\right)$
negative_passages.docid: 94466
negative_passages.text: evaluating the limit $ \lim_{(x,y) \rightarrow (0,0) } \frac{x^2y^2}{x^2 + y^2} $
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: 104996
negative_passages.text: Limit of $\lim_{n\rightarrow \infty} \sum^{n}_{i=1} \frac{1}{\sqrt {n^2 +i} }$
negative_passages.docid: 122769
negative_passages.text: Show that $\lim_{n\to \infty}\int_{[0,\infty]}\left(1+\dfrac{x}{n}\right)^n\exp(-ax)=\dfrac{1}{a-1}$
negative_passages.docid: 20089
negative_passages.text: Prove that $\lim_{N\rightarrow\infty}(1/N)\sum_{n=1}^N f(nx)=\int_{0}^1f(t)dt$
negative_passages.docid: 122073
negative_passages.text: Computing $\lim_{n \rightarrow\infty} \int_{a}^{b}\left ( f(x)\left | \sin(nx) \right | \right )$ with $f$ continuous on $[a,b]$
negative_passages.docid: 48891
negative_passages.text: Show that: lim$_{n\rightarrow \infty}\,f(x_n)=f(\text{lim}_{n \rightarrow \infty} \, x_n)$
negative_passages.docid: 95921
negative_passages.text: Question about $\lim _{q \rightarrow \infty}\|f\|_{q}=\|f\|_{\infty}$