Question

Write a in the form a = a T+an N at the given value of t without finding T and N. r(t) = (bet cos t) i + (6 et sin t)j + (6 et 13)k, t=0 a(0) = ( 1+ (ON (Type exact answers, using radicals as needed.)

Answer 1

given s (t) = 1 fet cost) it coetsint}; A t [bet 3.) E Conditions : 4:50. act zo) = ? . we know that uz de viz dads ds de (3 Acidding to chain rule ) V = TIT 1. dt de la des de fa

A we know that I dt an -EKN - den + de ani compuse above Equation i a = ant aut Cara k./ds) ² 1 an = des diz VF de . dela ing = dffet cost it set sint ftoss et  7 =b[etost + Esint)etyî +65 tsint + et cost.Jſ + 308 et Ã

aset stmt - G467 +6e(start Wlv = v(bet (Sint-646)] 27 [ce" ( stnt + cost)] + bvs et) (Vi= 130€€€ (sin’e +] + 34 (62) J.1+3 .Ge (2) N = Reto We know that a = d lul ③ ap = raet - a -la -

a=d16et (binet- cast dit bet( sind + st) +65etik) dt. . Telet (sint - ast) f (cost tsinty 7 treet (sint + 6st) 4 6c*[-sinet ost]]i + 6 S3 e lai= azt ay ta? a = bet Casint) î toe (2 Engt) + GV3 et = laet (sint) î+ laet (CASEL) +(633 et) Ê a = let (sint) + 12e" (Cost-)j + bugetare lal Vlaet sint)*7 (2ct Gast) (653 et je : - Jeny eRt + (34/3) et las = és 3424 +3143 = 6* + lo leer v Sony TORS

We know that an = v lase at al = 6 en t=o al. = 657 tro L 14-650 a = (betri) ² (12. (F) ² ( aje la es from ®) al = RV: 0 Ilt=0 a a a. Ntant from ② & 6 a = (laet) N +(6653)T

a = (12.) + (6 6 853) When too from ② 4 0 1 fal = (12) +(633)