考研数学笔记 - 等价无穷小

考研中常用的一些等价无穷小

Posted by Oscaner on September 9, 2018
\[\begin{align*} \sin x &\sim x \\ \arcsin x &\sim x \\ \tan x &\sim x \\ \arctan x &\sim x \\ e^x-1 &\sim x \\ \ln(1+x) &\sim x \\ \sqrt{1+x}-\sqrt{1-x} &\sim x \\ (1+ax)^b-1 &\sim abx \end{align*}\]
\[\begin{align*} 1-\cos x &\sim \dfrac{1}{2}x^2 \\ x-\ln(1+x) &\sim \dfrac{1}{2}x^2 \end{align*}\]
\[\begin{align*} \tan x-x &\sim \dfrac{1}{3}x^3 \\ x-\arctan x &\sim \dfrac{1}{3}x^3 \\ x-\sin x &\sim \dfrac{1}{6}x^3 \\ \arcsin x-x &\sim \dfrac{1}{6}x^3 \\ \tan x-\sin x &\sim \dfrac{1}{2}x^3 \end{align*}\]