高等数学中常用的等价无穷小

当 $x\rightarrow0$ 时

(01) $sin x \backsim x$

(02) $tan x \backsim x$

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