ln( 1+x)=x-x^2/2+x^3/3+.+(- 1)^(n- 1)*x^n/n+0(x^n)

0 (x n) is the higher order infinitesimal of x n.

Let x = 3x 2-2x be the expansion of ln [1+(3x 2-2x)].

In postgraduate mathematics, Taylor formula is mainly used in calculating limit, higher derivative and some proof problems, and some contents of Taylor formula will also be used in infinite series in the next volume.

In mclaughlin's formula,

Error |R? (x)| is the ratio of x when x→0? Higher order infinitesimal. ?

If the function f(x) has a derivative up to n+ 1 in the open interval (a, b), when the function is in this interval, it can be expanded into the sum of a polynomial about x and a remainder. His main contribution to algebra is that in algebraic theory (1748, the last work), he created a determinant method for solving simultaneous linear equations with multiple unknowns. But the narrative method in the book is not very good. Later, another mathematician, Clem, rediscovered this law, so it was called Clem's Law.