全部书籍

1 Primary & Middle School Mathematics1–9 年级在线 2 High School Mathematics10–12 年级在线 3 University Mathematics — Year 1本科一年级在线 4 University Mathematics — Year 2本科二年级在线 5 University Mathematics — Year 3本科三年级在线

1 Primary & Middle School Physics1–9 年级在线 2 High School Physics10–12 年级在线 3 University Physics — Year 1本科一年级在线 4 University Physics — Year 2本科二年级在线 5 University Physics — Year 3本科三年级在线

1 School Chemistry — Grades 1 to 121–12 年级在线 2 University Chemistry — Year 1本科一年级在线 3 University Chemistry — Year 2本科二年级在线 4 University Chemistry — Year 3本科三年级在线

1 Primary & Middle School Biology1–9 年级在线 2 High School Biology10–12 年级在线 3 University Biology — Year 1本科一年级在线 4 University Biology — Year 2本科二年级在线 5 University Biology — Year 3本科三年级在线

1 Primary & Middle School Earth and Space Sciences1–9 年级在线 2 High School Earth and Space Sciences10–12 年级在线 3 University Earth and Space Sciences — Year 1本科一年级在线 4 University Earth and Space Sciences — Year 2本科二年级在线 5 University Earth and Space Sciences — Year 3本科三年级在线

1 Markets I: The Ecosystem and Exchange-Traded Markets市场在线 2 Markets II: Rates, FX and Credit市场在线 3 Markets III: Commodities, Energy and Crypto市场在线 4 Quantitative Methods方法在线 5 Derivatives and Volatility衍生品在线 6 Rates, Credit, XVA and Risk利率、信用与风险在线 7 Research Craft: Predictors, Backtests, Measurement, Portfolios研究在线 8 Strategies I: Equities and Futures策略在线 9 Strategies II: Volatility, Relative Value, Macro and the Bank Desks策略在线 10 Microstructure and Execution交易执行在线 11 Market Making and High-Frequency Trading做市在线 12 Machine Learning for Markets机器学习在线 13 Low-Latency Software技术在线 14 Networks, Hardware and Trading Infrastructure技术在线 15 Research, Data and Risk Platforms技术在线 16 The Desk and the Firm公司运营在线 17 The Industry: Firms, Roles and Careers职业发展在线 18 Interviews I: Maths, Probability and Speed职业发展在线 19 Interviews II: Markets, Trading Games and the Final Round职业发展在线 20 Interviews III: Code职业发展在线

全部游戏 Math Fuse Word Reactor Atlas Dash

应用关于

Coach

English Français Español Nederlands Português हिन्दी العربية Bahasa Indonesia 简体中文 বাংলা

登录开始阅读

书籍暂未推出简体中文版——当前显示英文版。

Mathematics · 术语表

什么是 Sign table？

Definition 2.15 High School Mathematics · 第 2 章 — Algebra: Equations and Inequalities

A sign table records, on one row per factor, the sign ( $+$ or $-$ ) of each factor of an expression as $x$ runs over $\R$ , with a $0$ at each value where the factor vanishes; a final row gives the sign of the product, using the rule of signs column by column.

The graph of P(x) = (x-2)(3-x) confirms the sign table: positive between the roots 2 and 3, negative outside. — The graph of $P(x) = (x-2)(3-x)$ confirms the sign table: positive between the roots $2$ and $3$ , negative outside.

示例

Example 2.16

Sign of $P(x) = (x - 2)(3 - x)$ . The factor $x - 2$ vanishes at $2$ and is positive after; the factor $3 - x$ vanishes at $3$ and is positive before:

$x$	$-\infty$	$2$		$3$	$+\infty$
$x - 2$	$-$	$0$	$+$		$+$
$3 - x$	$+$		$+$	$0$	$-$
$P(x)$	$-$	$0$	$+$	$0$	$-$

So $P(x) > 0$ exactly on $\intoo{2}{3}$ , and $P(x) \leq 0$ on $\intoc{-\infty}{2} \cup \intco{3}{+\infty}$ .

Example 2.18

Solve $\dfrac{x + 1}{x - 3} \leq 0$ . The numerator vanishes at $-1$ , the denominator at $3$ (forbidden value). The quotient is negative when the two have opposite signs, which happens for $x$ between $-1$ and $3$ . Including the bound where the numerator vanishes but excluding the forbidden value: the solution set is $\intco{-1}{3}$ .

在原文中阅读 →