Exercicios resolvidos James Stewart vol. 2 7ª ed - ingles

298 D CHAPTER 15 PROBLEMS PLUS
To evaluate this sum, we first write out a few tenns: s = 1 - ; 3
+ ; 3
- ; 3
+ ;~ - ; 3
~ 0.8998. Notice that
a1 = \ < 0.003. By the Alternating Series Estimation Theorem from Section 11.5, we have Is- s61 ~ a1 < 0.003.
. 7 .
This error of0.003 :-viii not affectlhe second decimal place, so we have s .~ 0.90.
. au. 8u ox au ay au az au au. .
9. (a)x=rcosO, y =rsiDO, z=z. Then or= axar + ayar + ozor =ox cosO+ oysmOand
S . . 1
I ou ou . (} 8u (} d
lffil ary {)(} =-ax TSID + oy rcos an
8 2 u a 2 u ' 2 . 2
0
8 2 u. 2 2 8 2 u 2 . au 8u .
ao2 = 8x2 r SID + 8y2 r cos (} - 2 oy ax r SID 0 cos (} - OX r cos (} - {}y r SID 0. So
8 2 u lau 1 8 2 u _ 8 2 u a 2 u 2 8 2 u . 2 a 2 v. . au cosO 8u sinO
!:i:2 + - -a + 2 o2 + !i'2 = !i"2 cos 0 + !i'2 sm 0 + 2 .