query: Help show $\lim \limits_{p \to \infty }\frac{{\int_0^1 {|f{|^{p+1}}dx} }}{{\int_0^1 {|f{|^p}dx} }}$ if $f \in {L^\infty }[0,1]$
positive_passages.docid: 13486
positive_passages.text: Show $\lim \limits_{n \to \infty} \frac{a_{n+1}}{a_n} = \|f\|_{\infty}$ for $f \in L^{\infty}$
negative_passages.docid: 153267
negative_passages.text: Proving $\lim\limits_{x \to \infty} xf(x)=0$ if $\int_{0}^{\infty}f(x) dx$ converges.
negative_passages.docid: 86843
negative_passages.text: Find the value of : $\lim_{n\to\infty}[(n+1)\int_{0}^{1}x^{n}\ln(1+x)dx]$.
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: 89421
negative_passages.text: Does $\int_{1}^{\infty} g(x)\ dx$ imply $\lim\limits_{x\to \infty}g(x)=0$?
negative_passages.docid: 138169
negative_passages.text: Finding $\lim\limits_{n \to \infty }n\int_{0}^{1}\frac{x^{n}}{1+x+x^{n}}dx$
negative_passages.docid: 65015
negative_passages.text: Computing $\lim_{n \to \infty} \sqrt[n]{ \int_{0}^{1} (1+x^n)^n dx}$
negative_passages.docid: 25206
negative_passages.text: How to prove that $\lim\limits_{n\to \infty}a_{n+1}=\lim\limits_{n\to \infty}a_{n}$
negative_passages.docid: 119145
negative_passages.text: $\lim\limits_{n\rightarrow\infty} \sqrt{n}(\sqrt{n+1}-\sqrt{n})$
negative_passages.docid: 20764
negative_passages.text: Is it true that $\lim\limits_{x\to\infty}{x·P[X>x]}=0$?
negative_passages.docid: 143227
negative_passages.text: Show that: $\lim \limits_{n\to\infty}\frac{x_n-x_{n-1}}{n}=0 $
negative_passages.docid: 42817
negative_passages.text: proving $\lim\limits_{n\to\infty} \int_{0}^{1} f(x^n)dx = f(0)$ when f is continous on [0,1]
negative_passages.docid: 57600
negative_passages.text: Show $\lim\limits_{a \rightarrow + \infty} \int_0^{\infty} \frac{1}{1+y^2}e^{-ay} dy =0 $
negative_passages.docid: 117246
negative_passages.text: Show that $\lim\limits_{a \to 0^+} \int^1_0 ax^{a−1}f(x)dx=f(0)$.
negative_passages.docid: 50682
negative_passages.text: Prove: $\lim\limits_{n \to \infty} \int_{0}^{\sqrt n}(1-\frac{x^2}{n})^ndx=\int_{0}^{\infty} e^{-x^2}dx$
negative_passages.docid: 113289
negative_passages.text: finding the limit $\lim\limits_{x \to \infty }(\frac{1}{e}(1+\frac{1}{x})^x)^x$