Question

-US Help 1 System Announcements Anton, Calculus! Early Transcendentals, lle Start Time: 10:47 PM / Remaining: 79 min. ES Question 2 Find T() and N(t) at the given point. x = e' cost, y = e' sint, z = e'; t = 0 Enter the vector i as $7, the vector jas 7, and the vector k as T(0) = Edit N(0) = Edit

Answer 1

Given rit) = < x 1t), ylt), zlu? <etcost, etsint, ety 81H) = we know. d et cost Unit tangent vector is given by tilt) Tit) = 810) lat etcast tetſ-sint) How de g'lt) = dretcost, etsint, et a refsint)= etsint + etcost dt re etcost-efsint, et sint tetcost, et> at t=0, t'10) = < e°w30-eºsino, eºsinoteºcolo, eº> Y'(0) = < 1, 61,17 Ir'(o)l 51*+1+1° 53 T (A) = rllo) < 1, 1, 1> 53 <še ? اره 7 | TOO) = 5 i + ts + FR rat

Unit Normal vector is given by Nit) - T'lt) IT'le Tit) . t е. gilt) s et caust-sint), et sint+cost), ety 18'() Jleticot sint))*+ (et (simeteost)? Het) · <et (cost-sint), et (hint twost),ety Wat+Sin't-2.cosefinit Sirittuoit + 2 sintlost + Ket(cost-sint), eti sinetcost), et et 3. sin't Host=1 - 53 + L cost-sint sint that TIE) / = How of (sinttust) T'(t) = d. TU) = dt to (cost-sint), It 3 dt > dt of cost - sint), o> (-sint-Cost) I at t=0 T10) = rsa 1-0-1), tã 11-0), o) T'(0) = p < Joy

(Tio) | = () + (+(c) 十 支 + 3 (三 定点 人。 < N[0) T'o) IT']} JS JX. N(0) 〈点, > 1 614 ( 7g 上E |o> NO) 后, N(6) Ii 走 b