Question

Question 17 Calculate the arc length of the curve r(t) = (cos: t)+ (sin t)k on the interval 0 <ts. Question 18 Find the curvature of the curve F(t) = (3t)i + (2+2)ż whent = -1. No new data to save. Last checked a

Answer 1

M 8(t) = 68 ) ) + (sin tk on octe II filt) = (-3 cost sint)j + (3 sin²t costk lo' (t) || = 56-3 capit sint) 2 + (3 sin²t cost)? = √ a capitain't ta sinut cost - 9 ein't coat (con't + sin’t) ar asint cost [ " cos?tt sin?t=]] = 3 sint coft So, are length = 2 1 110 (t) ll at C = l zsintcost dt 11 3 ssint costat singt dt 2 J = -3 [coß2t), soli je are length = 1 2 3 a ® Find curvature of g It) = (st)i + (2+²); when t=-), 8 (t) = 3i+ utg. unit tangent vector Pt) = (vatnog 7' (t) = (ce type ( 9+164)% l/x' (t) || = 59+16+ , l18'(-1) || = 5 २

IT' (t) 1 = [(-48t) ² t 8 – V (9+16 +2) Cat16+213 TITLED| + eness 477 2385 477 V 525 (25) 2 The curvature is k = = 477 XL 11T'(-1) 11 llo!(-01 . 25 5 5 le k = 0,078