1, sinx = x-1/6x3+o (x 3), these are sine expansions of Taylor formula, and sinx can be replaced by Taylor formula expansion when seeking the limit.

2. Arcsinx = x+1/6x3+o (x 3), which is the arcsine expansion of Taylor's formula. Arcsinx can be replaced by Taylor formula expansion when seeking the limit.

3.tanx = x+ 1/3x 3+O (x 3), which is the tangent expansion of Taylor's formula. Tanx can be replaced by Taylor formula expansion when seeking the limit.

4.arctanx = x- 1/3x 3+O (x 3), which is the arctangent expansion of Taylor formula. When seeking the limit, we can use Taylor formula expansion instead of Arctanx.

5. ln (1+x) = x-1/2x2+o (x2), which is the expansion of Taylor's formula. When seeking the limit, ln( 1+x) can be replaced by Taylor formula expansion.

6. Cosx =1-1/2x2+O (x2), which is the cosine expansion of Taylor's formula. When calculating the limit, Taylor formula expansion can be used instead of Cosx.