高等数学中常用的等价无穷小

x\rightarrow0

(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