若limα(x)/β(x)=1，则α(x)与β(x)是等价的无穷小，记作α(x) ~ β(x)
| sinx ~ x | arcsinx ~ x |
|---|---|
| tanx ~ x | arctanx ~ x |
| ln(1+x) ~ x | e^x-1 ~ x |
| 1-cosx ~ 1/2x² | (1+x)^(1/n)-1 ~ (1/n)x |
| 1-cosx^α ~ α/2x² | |
| a^x-1 ~ xlna | x-sinx ~ (1/6)x³ |
| x+sinx ~ 2x | arcsinx-x ~ (1/6)x³ |
| arcsinx+x ~ 2x | tanx-x ~ (1/3)x³ |
| x-arctanx ~ (1/3)x³ | tanx-sinx ~ (1/2)x³ |
| x-ln(1+x)~(1/2)x² | e^α-e^β ~ α-β |
当x->1时
| lnx ~ x-1 |
|---|
