高等数学

当 $x\rightarrow0$ 时：$\tan x$ $\backsim$ $x$$\sin x$ $\backsim$ $x$$\arcsin x$ $\backsim$ $x$$\arctan x$ $\backsim$ $x$$\ln(1+x)$ $\backsim$ $x$$e^{x} -1$ $\backsim$ $x$$1-\cos x$ $\backsim$ $\frac{1}{2}x^{2}$$x – \ln(1 + x)$ $\backsim$ $\frac{1}{2}x^{2}$$\tan x – \sin x$ $\backsim$ $\frac{1}{2}x^{3}$$\arcsin x – \arctan x$ $\backsim$ $\frac{1}{2}x^{3}$$\tan x – x$ $\backsim$ $\frac{1}{3}x^{3}$$x – \arctan x$ $\backsim$ $\frac{1}{3}x^{3}$$x – \sin x$ $\backsim$ $\frac{1}{6}x^{3}$$(1+x)^{a}-1$ $\backsim$ $ax$$a^{x}-1$ $\backsim$ $\ln a\times x$

(01) 当 $\beta(x)$ $\rightarrow$ $0$ 且 $\beta(x) \cdot \alpha(x)$ $\rightarrow$ $0$ 时：$[1 + \beta(x)]^{\alpha(x)} – 1$ $\sim$ $\alpha(x) \beta(x)$