高等数学中常用的等价无穷小

当 $x\rightarrow0$x→0 时

(01) $sin x \backsim x$sinx∽x

(02) $tan x \backsim x$tanx∽x

(03) $arcsin x \backsim x$arcsinx∽x

(04) $arctan x \backsim x$arctanx∽x

(05) $ln(1+x) \backsim x$ln(1+x)∽x

(06) $e^{x} -1 \backsim x$ex−1∽x

(07) $1-cos x \backsim \frac{1}{2}x^{2}$1−cosx∽21​x2

(08) $x - ln(1 + x) \backsim \frac{1}{2}x^{2}$x−ln(1+x)∽21​x2

(09) $tan x - sin x \backsim \frac{1}{2}x^{3}$tanx−sinx∽21​x3

(10) $arcsin x - arctan x \backsim \frac{1}{2}x^{3}$arcsinx−arctanx∽21​x3

(11) $tan x - x \backsim \frac{1}{3}x^{3}$tanx−x∽31​x3

(12) $x - arctan x \backsim \frac{1}{3}x^{3}$x−arctanx∽31​x3

(13) $x - sin x \backsim \frac{1}{6}x^{3}$x−sinx∽61​x3

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

(15) $a^{x}-1 \backsim lna\times x$ax−1∽lna×x

标签：frac,sinx,无穷小,tanx,等价,backsim,arctanx,x3,高等数学
来源： https://blog.csdn.net/wy_bk/article/details/91353114