able 1. 1 Taylor Series Expansions for Some Common Functions sin(a)=a + + for all a 6 cos( )=1 ×y for all e=1+x ×乙3 +,+,+ TOr 2!3!4! In(1+.)=a + 1<x<1 arctan( =a + 1<x<1 +2=1++(p-1)2 +… for la|<1
Table 1.2 partial sums s used to Determine e Sn=1++3+…+ n012345678901 2.5 2.666666666666.. 2.708333333 2.716666666666 2.718805555555. 2.71825:968254 2.718278769841. 2.718281525573. 2.718281801146 2.718281826199. 2.718281828286 13 2.718281828447. 14 2.718281828458. 15 2.718281828459