Headings

常用的等价无穷小

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book
math
高等数学
book
math
高等数学

常用的等价无穷小

J.Gong

2021-05-07

0.31min

常用的等价无穷小

lim⁡x→0sin⁡x∼xlim⁡x→0tan⁡x∼xlim⁡x→0arcsin⁡x∼xlim⁡x→0arctan⁡x∼xlim⁡x→0ln⁡(1+x)∼xlim⁡x→0(ex−1)∼xlim⁡x→0(ax−1)∼xln⁡alim⁡x→0(1−cos⁡x)∼12x2lim⁡x→0[(1+x)a−1]∼ax\lim_{x \to 0}\sin x \sim x \\ \lim_{x \to 0}\tan x \sim x \\ \lim_{x \to 0}\arcsin x \sim x \\ \lim_{x \to 0}\arctan x \sim x \\ \lim_{x \to 0}\ln(1+x) \sim x \\ \lim_{x \to 0}(e^x-1) \sim x \\ \lim_{x \to 0}(a^x-1) \sim x\ln a \\ \lim_{x \to 0}(1-\cos x) \sim \frac{1}{2} x^2 \\ \lim_{x \to 0}[(1+x)^a-1] \sim ax