Table 1.1 Taylor Series Expansions for Some Common Functions Sin( r= ′×25 + or all r 4x6 cos(a=1 + TOr 4!6 e=1+x+-+++ 3!4 n(1+x)=x C乙 3 + 1<x<1 234 arctan(a)=a + 1<x<1 35 +x)2=1+mD-1)2 +… for ac|<1
Table 1.2 Partial sums s used to determine e Sn=1+++…+ n0123456789 2.0 2.5 2.666666666666 2.708333. 2.716666666666 2.718805555555 2.718253968254 2.718278769841 2.718281525573 2.718281801146. 2.718281826199 12 2.718281828286 13 2.718281828447. 14 2.718281828458.. 15 2.718281828459