线性代数公式汇总2021-09-062021-09-07学习2 分钟读完 (大约332个字) 行列式 ∣AT∣=∣A∣;∣kA∣=kn∣A∣;∣AB∣=∣A∣∣B∣;∣A∗∣=∣A∣n−1;∣A−1∣=∣A∣−1=1∣A∣;A∼B⟶∣A∣=∣B∣.\begin{aligned} & \large |A^T|=|A|; \quad\quad\quad\quad |kA|=k^n|A|;\\ & \large |AB|=|A||B|; \quad\quad\quad\quad |A^*|=|A|^{n-1};\\ & \large |A^{-1}|=|A|^{-1}=\frac{1}{|A|}; \quad\quad\quad\quad A\sim B \longrightarrow |A|=|B|.\\ \end{aligned} ∣AT∣=∣A∣;∣kA∣=kn∣A∣;∣AB∣=∣A∣∣B∣;∣A∗∣=∣A∣n−1;∣A−1∣=∣A∣−1=∣A∣1;A∼B⟶∣A∣=∣B∣.阅读更多
高等数学公式汇总2021-03-302021-09-06学习12 分钟读完 (大约1766个字) 等价无穷小 sinx∼tanx∼arcsinx∼arctanx∼ln(1+x)∼ex−1∼xx−sinx∼16x3x−arcsinx∼−16x3x−tanx∼−13x3x−arctanx∼−13x31−cosx∼12x21−cosax∼a2x2ax−1∼xlna(1+x)a−1∼ax\begin{aligned} & \large \sin{x} \sim \tan{x} \sim \arcsin{x} \sim \arctan{x} \sim \ln(1+x) \sim \text{e}^x-1 \sim x \\ & \large x-\sin{x} \sim \frac{1}{6}x^3 \quad\quad\quad\quad x-\arcsin{x} \sim -\frac{1}{6}x^3 \\ & \large x-\tan{x} \sim -\frac{1}{3}x^3 \quad\quad\quad\quad x-\arctan{x} \sim -\frac{1}{3}x^3 \\ & \large 1-\cos{x} \sim \frac{1}{2}x^2 \quad\quad\quad\quad 1-\cos^ax \sim \frac{a}{2}x^2 \\ & \large a^x-1 \sim x\ln a \quad\quad\quad\quad (1+x)^a-1 \sim ax \\ \end{aligned} sinx∼tanx∼arcsinx∼arctanx∼ln(1+x)∼ex−1∼xx−sinx∼61x3x−arcsinx∼−61x3x−tanx∼−31x3x−arctanx∼−31x31−cosx∼21x21−cosax∼2ax2ax−1∼xlna(1+x)a−1∼ax阅读更多