query: Prove $\sin(kx) \rightharpoonup 0$ as $k \to \infty$ in $L^2(0,1)$
positive_passages.docid: 157422
positive_passages.text: Why $\sin(nx)$ converges weakly in $L^2(-\pi,\pi)$?
negative_passages.docid: 133874
negative_passages.text: Proof that $\lim_{n\to\infty}{\sin{100n}}$ does not exist
negative_passages.docid: 95673
negative_passages.text: General formula for $\sin\left(k\arcsin (x)\right)$
negative_passages.docid: 149827
negative_passages.text: show that $x\sin\left(\frac{1}{x}\right)$ is uniformly continuous on $(0,1)$
negative_passages.docid: 53831
negative_passages.text: Find a general solution for $\int_{0}^{\infty} \sin\left(x^n\right)\:dx$
negative_passages.docid: 21589
negative_passages.text: Prove the divergence of the sequence $\left\{ \sin(n) \right\}_{n=1}^{\infty}$.
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: 102918
negative_passages.text: Prove $\sin x$ is uniformly continuous on $\mathbb R$
negative_passages.docid: 91278
negative_passages.text: The limit for $x\to 0$ of $x^3\sin (x)$ exists
negative_passages.docid: 72266
negative_passages.text: Prove that $\lim_{j \to\infty}\sum_{k = 1}^{\infty} \frac{a_k}{j+k} = 0$
negative_passages.docid: 142637
negative_passages.text: If $f \in \mathcal{L}^1(\mathbb{R})$ then $\lim_{h\rightarrow 0}\int_{-\infty}^\infty |f(x+h)-f(x)|dx\rightarrow 0$
negative_passages.docid: 90556
negative_passages.text: Proof of the unbounded-ness of $\sum_{n\geq 1}\frac{1}{n}\sin\frac{x}{n}$
negative_passages.docid: 38185
negative_passages.text: Prove that $\{\cos(nx) : n=1, ... ,\infty \}$ is bounded but not totally bounded in $C([0,\pi])$
negative_passages.docid: 83790
negative_passages.text: Why doesn't $d(x_n,x_{n+1})\rightarrow 0$ as $n\rightarrow\infty$ imply ${x_n}$ is Cauchy?
negative_passages.docid: 83703
negative_passages.text: Show that $\int_{0}^{\infty}|\frac{\sin x}{x}|\,dx=\infty $
negative_passages.docid: 23288
negative_passages.text: Prove that $x^2<\sin x \tan x$ as $x \to 0$
negative_passages.docid: 77322
negative_passages.text: Uniform continuity of $\sin(x\sin x )$ for all $x\in (0,\infty)$