1. The document is about Taylor polynomials for the function x e^-x. 2. It gives the Taylor series expansion for x e^-x and lists the first 20 Taylor polynomials P1(x) through P20(x). 3. Readers are asked to graph the function x e^-x along with its Taylor polynomials of varying degrees to compare how well the polynomials approximate the original function.

1. 1
國立中央大學數學系
Taylor 多項式 : 習題 3
 畫出 x 𝐞−𝐱
不同次數 Taylor 多項式的函數圖:
 X 𝐞−𝐱
= x -
𝐱𝟐
𝟏!
+
𝐱𝟑
𝟐!
-
𝐱𝟒
𝟑!
+ . . . + (−𝟏)𝐤−𝟏 𝐱𝐤
𝐤−𝟏 !
k≥1
𝐏𝟏(X)、𝐏𝟐(X)、𝐏𝟑(X)、. . . 、𝐏𝟐𝟎(X)
𝐏𝟏 𝐗 = X
𝐏𝟐 𝐗 = X － 𝐗𝟐
𝐏𝟑 𝐗 = X － 𝐗𝟐 +
𝐗𝟑
𝟐

2. 2
國立中央大學數學系
Taylor 多項式 : 習題 3