query: Explain why $| e^{iwx} - 1 | \le 2 |w| \, |x|$
positive_passages.docid: 108995
positive_passages.text: Prove $|e^{i\theta} -1| \leq |\theta|$
negative_passages.docid: 54380
negative_passages.text: Prove if $|z| < 1$ and $ |w| < 1$, then $|1-zw^*| \neq 0$ and $| {{z-w} \over {1-zw^*}}| < 1$
negative_passages.docid: 107774
negative_passages.text: Prove $\|x\|_1\le \sqrt n \|x\|_2$
negative_passages.docid: 15300
negative_passages.text: How to show that $(W^\bot)^\bot=W$ (in a finite dimensional vector space)
negative_passages.docid: 158610
negative_passages.text: Why is the differentiation of $e^x$ is $e^x$?
negative_passages.docid: 122115
negative_passages.text: Proving that $1+x^py^{1-p} \le (1+x)^p(1+y)^{1-p}$
negative_passages.docid: 149634
negative_passages.text: $ 2|f^{'}(0)| = \sup_{z, w \in D} |f(z)-f(w)|$
negative_passages.docid: 103536
negative_passages.text: How to prove $|e^{i\theta} - 1| \leq |\theta|$?
negative_passages.docid: 147590
negative_passages.text: If $L$ is regular, prove that $\sqrt{L}=\left\{ w : ww\in L\right\}$ is regular
negative_passages.docid: 95415
negative_passages.text: proof relating to limit definition of e
negative_passages.docid: 14576
negative_passages.text: $(U\cap W)^0 = U^0 + W^0$
negative_passages.docid: 46746
negative_passages.text: How to prove if $u\in W^{1,p}$, then $|u|\in W^{1,p}$?
negative_passages.docid: 107254
negative_passages.text: Real analysis question $e^{-1/x^2}$
negative_passages.docid: 5350
negative_passages.text: Explain why $E(|X|^p)=p\int_{0}^{\infty}y^{p-1}P(|X|>y) dy$
negative_passages.docid: 40837
negative_passages.text: Why $e^{i(π/3)} \ne -1$?
negative_passages.docid: 132920
negative_passages.text: Help with proof that the expected value of $x_i$ is $\bar{X}$
negative_passages.docid: 97253
negative_passages.text: How prove $e^x|f(x)|\le 2$ if $f(x)=\int_{x}^{x+1}\sin{(e^t)}dt$