query: Calculate $\lim_{n \to \infty} \int_0^1nx^nf(x)dx$.
positive_passages.docid: 145233
positive_passages.text: How to show $\lim_{n \rightarrow \infty} \int_0^1 n x^n f(x) \; dx = f(1)$ for continuous $f$?
negative_passages.docid: 39798
negative_passages.text: Computing $\lim_{n \to \infty} \int_0^{n^2} e^{-x^2}n\sin\frac{x}{n}\,dx$?
negative_passages.docid: 114372
negative_passages.text: Calculate $\lim_{t\to\infty}\frac 1t\log\int_0^1 \cosh(tf(x))\mathrm d x$
negative_passages.docid: 92176
negative_passages.text: Solving $\lim_{n\to\infty}(n\int_0^{\pi/4}(\tan x)^ndx)$?
negative_passages.docid: 152557
negative_passages.text: Calculate $ \lim\limits_{n \to \infty} \sum\limits_{k=0}^n \frac{2^{k-1}}{a^{2k-1}+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: 45737
negative_passages.text: Limit $\lim_{n \to \infty} \frac{n!}{n^n}$
negative_passages.docid: 96505
negative_passages.text: Compute $\int_0^\infty \left(\frac{1}{x}\right)^{\ln(x)}\,\mathrm{d}x$
negative_passages.docid: 49489
negative_passages.text: Compute $\lim_{n\to\infty} \int_{0}^{\pi/4}\tan^n x \ dx$
negative_passages.docid: 46156
negative_passages.text: How to find $\lim_{x \to \infty} [x]/x$?
negative_passages.docid: 44054
negative_passages.text: Evaluating the integral $\mathop{\lim}\limits_{n \to \infty} \int_{-1}^{1} f(t)\cos^{2}(nt) \ dt $
negative_passages.docid: 97256
negative_passages.text: For $f$ continuous, show $\lim_{n\to\infty} n\int_0^1 f(x)x^n\,dx = f(1).$
negative_passages.docid: 151149
negative_passages.text: $\lim_{n \to \infty} n \int_{1}^{\infty} \frac{dx}{1+x^n}$, solution critique needed
negative_passages.docid: 124699
negative_passages.text: How to calculate $\lim_{n \to \infty}\sqrt[n]{\frac{2^n+3^n}{3^n+4^n}}$
negative_passages.docid: 145903
negative_passages.text: Prove that $\int_E |f_n-f|\to0 \iff \lim\limits_{n\to\infty}\int_E|f_n|=\int_E|f|.$
negative_passages.docid: 117497
negative_passages.text: Compute the limit $\lim_{n \to \infty} \frac{n!}{n^n}$
negative_passages.docid: 25193
negative_passages.text: Find $ \lim _{n\to \infty} \frac{n^1+\dots+n^n}{1^n+\dots+n^n}$