query: Derivation of this inequality
positive_passages.docid: 16852
positive_passages.text: $|e^a-e^b| \leq |a-b|$ for complex numbers with non-positive real parts
negative_passages.docid: 116685
negative_passages.text: Reciprocal of Holder's inequality
negative_passages.docid: 108704
negative_passages.text: Help with proof of $|x+y| \geq |x|-|y|$
negative_passages.docid: 138959
negative_passages.text: On the equality case of the Hölder and Minkowski inequalities
negative_passages.docid: 7404
negative_passages.text: Induction and convergence of an inequality: $\frac{1\cdot3\cdot5\cdots(2n-1)}{2\cdot4\cdot6\cdots(2n)}\leq \frac{1}{\sqrt{2n+1}}$
negative_passages.docid: 26828
negative_passages.text: Generalization of Hölder inequality
negative_passages.docid: 115335
negative_passages.text: How can we prove this integral inequality?
negative_passages.docid: 143968
negative_passages.text: Proving this inequality by mathematical induction
negative_passages.docid: 5465
negative_passages.text: This inequality $a+b^2+c^3+d^4\ge \frac{1}{a}+\frac{1}{b^2}+\frac{1}{c^3}+\frac{1}{d^4}$
negative_passages.docid: 65168
negative_passages.text: Proof of sequence inequality
negative_passages.docid: 132595
negative_passages.text: $\sup_{0 \leq M \leq I_{\mathcal{H}_1}} \frac{\operatorname{Tr}[\rho M]}{\operatorname{Tr}[\sigma M]}$ satisfies Data Processing Inequality
negative_passages.docid: 71497
negative_passages.text: An inequality from Littlewood's Miscellany
negative_passages.docid: 158576
negative_passages.text: Derivation of the quadratic equation
negative_passages.docid: 147785
negative_passages.text: Proving inequality $x^xy^y \geq (\frac{x+y}{2})^{x+y}$
negative_passages.docid: 101792
negative_passages.text: By expanding $e^x$ into a series prove the following inequality
negative_passages.docid: 91871
negative_passages.text: Proving quadratic inequalities?
negative_passages.docid: 15237
negative_passages.text: Prove an inequality using complex analysis