考研数学:常见的等价无穷小替换

sin ⁡ x ∼ x \sin{\it x}\sim{\it x} sinxx

arcsin ⁡ x ∼ x \arcsin{\it x}\sim{\it x} arcsinxx

tan ⁡ x ∼ x \tan{\it x}\sim{\it x} tanxx

arctan ⁡ x ∼ x \arctan{\it x}\sim{\it x} arctanxx

ln ⁡ ( 1 + x ) ∼ x \ln(1+x)\sim{x} ln(1+x)x

e x ∼ x e^x\sim{x} exx

1 − cos ⁡ x ∼ x 2 2 1-\cos{x}\sim\frac{{\it x^2}}{{\it 2}} 1cosx2x2

( 1 + x ) u − 1 ∼ u x (1+x)^u-1\sim{ux} (1+x)u1ux

a x − 1 ∼ x ln ⁡ a a^x-1\sim{x\ln{a}} ax1xlna

l o g a ( 1 + x ) = x / ln ⁡ a log_{a}(1+x)=x/\ln a loga(1+x)=x/lna

你可能感兴趣的:(#,高等数学,考研,抽象代数)