query: If $f \in L^p(\mathbb{R})$ then $\lim_{x \rightarrow \infty} \int_x^{\infty} |f(t)|^pdt=0$
positive_passages.docid: 19072
positive_passages.text: $\int_{\mathbb R} |f(x)| dx < \infty \implies \int^{\infty}_{n} |f(x)| dx \to 0$ as $n \to \infty$?
negative_passages.docid: 41173
negative_passages.text: If $f\in S_\infty$ and $\int_{\mathbb{R}}x^pf(x)d\mu=0$ for all $p\in\mathbb{N}$ then $f\equiv 0$?
negative_passages.docid: 17019
negative_passages.text: Show that: $\lim\limits_{r\to\infty}\int\limits_{0}^{\pi/2}e^{-r\sin \theta}\text d\theta=0$
negative_passages.docid: 44129
negative_passages.text: If $f:\mathbb{R}\rightarrow \mathbb{R}$ is differentiable and $\lim_{x\to \infty } f^\prime(x)=0$ show that $\lim _{x\to \infty } (f(x+1)-f(x))=0$.
negative_passages.docid: 55173
negative_passages.text: Solve for $\lim_{x \rightarrow \infty} \frac{x^{\ln(x)}}{(\ln(x))^x}$
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: 88792
negative_passages.text: Convergence of $\int_0^\infty $sin$ (x^p) dx$
negative_passages.docid: 145233
negative_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: 27705
negative_passages.text: Proof of $\int_{[0,\infty)}pt^{p-1}\mu(\{x:|f(x)|\geq t\})d\mu(t)=\int_{[0,\infty)}\mu(\{x:|f(x)|^p\geq s\})d\mu(s)$
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: 10093
negative_passages.text: $\lim_{x\to \infty}e^{-x^2}\int_x^{x+1/x}e^{t^2}dt$
negative_passages.docid: 65662
negative_passages.text: Prove $\forall K > 0: \lim_{n\rightarrow\infty} \sqrt[n]{K} = 1$
negative_passages.docid: 124916
negative_passages.text: $f$ such that $\int_1^{\infty}f(x)dx$ converges, but not absolutely?
negative_passages.docid: 136738
negative_passages.text: Does the limit $\lim _{x\to 0} \frac 1x \int_0^x \left|\cos \frac 1t \right| dt$ exists?
negative_passages.docid: 8836
negative_passages.text: If $f$ is continuous on $[a , b]$ and $\int_a^b f(x) p(x)dx = 0$ then $f = 0$
negative_passages.docid: 54321
negative_passages.text: Questions about $f: \mathbb{R} \rightarrow \mathbb{R}$ with bounded derivative
negative_passages.docid: 110275
negative_passages.text: Let $p>0$. Show the $\lim_{n\to\infty}(a^n/n^p)$ is equal to: