我們利用python的sympy模塊能夠很方便的進行科學計算，可以利用它對變量表達式進行泰勒展開并繪制圖像，下面是我對sin(x)進行麥克勞林展開并繪制圖像

            
              from matplotlib import pyplot as plt
import numpy as np
from mpl_toolkits.mplot3d import Axes3D
from sympy import * #用于求導積分等科學計算
from sympy.plotting import plot3d
from sympy.functions import exp

x = Symbol('x')#x 變量
print(help(plot))#對x = 0點泰勒展開 至x20次方無窮小 

p0 = plot(sin(x),(x,-2*pi,2*pi),line_color='b',ylim=(-1.5,1.5),title='funion',show=False)
#畫出sin(x),范圍-2*pi,2*pi，藍色線，y刻度范圍-1.5,1.5，暫不顯示
exper1 = series(sin(x),x,n=4)#泰勒展開至第O(x**4)
p1 = plot(exper1.subs(O(x**4),0),(x,-2*pi,2*pi),line_color='br',title='O(x**4)',show=False)
#第O(x**4)項用0替代 顏色為藍紅色
exper2 = series(sin(x),x,n=6)#泰勒展開至第O(x**6)
p2 = plot(exper2.subs(O(x**6),0),(x,-2*pi,2*pi),line_color='g',title='O(x**6)',show=False)
#第O(x**6)項用0替代 顏色為綠
exper3 = series(sin(x),x,n=8)#泰勒展開至第O(x**8)
p3 = plot(exper3.subs(O(x**8),0),(x,-2*pi,2*pi),line_color='r',title='O(x**8)',show=False)
#第O(x**8)項用0替代 顏色為紅
exper4 = series(sin(x),x,n=10)#泰勒展開至第O(x**10)
p4 = plot(exper4.subs(O(x**10),0),(x,-2*pi,2*pi),line_color='y',title='O(x**10)',show=False)
#第O(x**10)項用0替代 顏色為黃
p0.extend(p1)
p0.extend(p2)
p0.extend(p3)
p0.extend(p4)
p0.show()#顯示圖像

            
          

運行結果

可以看到，隨著展開的項數越多，展開后的圖形就越接近藍線sin(x)?，黃線是展開至O(x**10)無窮小項的圖像

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