绝对值
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$\mid a \mid * \mid b \mid = \mid a b \mid$
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${\Large \mid \frac{a}{b} \mid } = {\Large \frac{\mid a \mid}{\mid b \mid} }$
不定积分
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$\int [\,f(x) \, \pm \, g(x) \, ]\, dx = \int f(x)\, dx \, \pm \, \int g(x) \, dx$
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$\int kf(x) \, dx = k\int f(x) \, dx$
极限
若 $\lim \, f(x)=A,\quad \lim \, g(x)=B$- $\lim \, [f(x) \pm g(x)]=A \pm B$
- $\lim \, [f(x)·g(x)] = A·B$
乘除是一起证明的，除是一样的
导数
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$\log_{a}MN =\log_{a}M+\log_{a}N$
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$\log_{a}\frac{M}{N} =\log_{a}M-\log_{a}N$
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$\log_{a}M^{n}=n\log_{a}M$
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$\log_{a}mM^{n}=\frac{n}{m}\log_{a}M$
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$\log_{a}b=\frac{\log_{c}b}{\log_{c}a}$