高等数学中常用的等价无穷小

当 $x\rightarrow0$ 时

(02) $ \tan x \backsim x $

(01) $ \sin x \backsim x $

(03) $ \arcsin x \backsim x $

(04) $ \arctan x \backsim x $

(05) $ \ln(1+x) \backsim x $

(06) $ e^{x} -1 \backsim x $

(07) $ 1-\cos x \backsim \frac{1}{2}x^{2} $

(08) $ x – \ln(1 + x) \backsim \frac{1}{2}x^{2} $

(09) $ \tan x – \sin x \backsim \frac{1}{2}x^{3} $

(10) $ \arcsin x – \arctan x \backsim \frac{1}{2}x^{3} $

(11) $ \tan x – x \backsim \frac{1}{3}x^{3} $

(12) $ x – \arctan x \backsim \frac{1}{3}x^{3} $

(13) $ x – \sin x \backsim \frac{1}{6}x^{3} $

(14) $ (1+a)^{x}-1 \backsim ax $

(15) $ a^{x}-1 \backsim \ln a\times x $