query: limit of sequence of integrals on [0,1]
positive_passages.docid: 97256
positive_passages.text: For $f$ continuous, show $\lim_{n\to\infty} n\int_0^1 f(x)x^n\,dx = f(1).$
negative_passages.docid: 39797
negative_passages.text: Convergence of integrals in $L^p$
negative_passages.docid: 107237
negative_passages.text: Evaluate $\lim_{n\rightarrow\infty} \int_0^1 f(x^n) dx$
negative_passages.docid: 129087
negative_passages.text: Proof that a sequence of continuous functions $(f_n)$ cannot converge pointwise to $1_\mathbb{Q}$ on $[0,1]$
negative_passages.docid: 27156
negative_passages.text: Sequence Limit: $\lim\limits_{n \rightarrow \infty}{n\,x^n}$
negative_passages.docid: 16228
negative_passages.text: Show that there is sequence of homeomorphism polynomials on [0,1] that converge uniformly to homeomorphism
negative_passages.docid: 34723
negative_passages.text: Proof of a limit for a recursively-defined sequence
negative_passages.docid: 1760
negative_passages.text: Limit of the geometric sequence $\{r^n\}$, with $|r| < 1$, is $0$?
negative_passages.docid: 150971
negative_passages.text: If $f$ is Riemann integrable on $[0,1]$ then $\lim\limits_{n\rightarrow\infty}\frac{1}{n}\sum f\left(\frac{k}{n}\right)=\int\limits_{0}^{1} f(x)dx$
negative_passages.docid: 114975
negative_passages.text: Limit of sequences $V(n)$ and $U(n)$
negative_passages.docid: 155475
negative_passages.text: $\lim\limits_{n\to \infty} \int_0^1 |f(x)-a_nx-b_n| dx=0$ implies $(a_n)_n,(b_n)_n$ are convergent
negative_passages.docid: 102523
negative_passages.text: Show that $\lim\limits_{n \to \infty} \sup\limits_{k \geq n} \left(\frac{1+a_{k+1}}{a_k}\right)^k \ge e$ for any positive sequence $\{a_n\}$
negative_passages.docid: 63608
negative_passages.text: Cauchy sequence in a normed space
negative_passages.docid: 140379
negative_passages.text: Cauchy sequence in a discrete space
negative_passages.docid: 69348
negative_passages.text: Prove that $\int \limits _{0}^{\infty}\frac{e^{-2x}-e^{-ax}}{x}\text{d}x$ converges for any $a>0$
negative_passages.docid: 123253
negative_passages.text: Limit of a sequence $a_1=1;a_{n+1}=(n+1)(1+a_n)$
negative_passages.docid: 138294
negative_passages.text: Increasing sequence of step functions and diverging Lebesgue Integrals