DRAM 115 Lecture 4: Twelfth Night

(1 point) Consider the integral dz. Which of the following expressions represents the integral as a limit of Riemann sums? TL A. lim 2+트 B. lim i-1 Tt 1n C. lim Tn D. lim 1-1 E. lim F. lim

cos Tn) In(n+1)

-/5 points LarCalc11 12.5.030. Find the curvature K of the curve r(t) -3 cos(at)i + sin(t)j 9 (sin (π t))2 + (cos (π t))2), K = (No Response) Solution or Explanation : r(t) 3 cos(t)i + sin(Tt)j : r'(t) =-3π sin(Tt)i + π cos(nt)j : lirtt)II = π/9 (sin(mt))2 + (cos(mt))2 -3 sin(it)i +cos(t)j : T(t)= 9 sin(t)) cos(t) 12 (t)- (9 (sin(Tt)) 2 3/2 + (cos(πt) 9sin(t)cos(t) llr()ll TV 9 (sin(rt)) + cos(rt) (9 (sin(Tt))+ (cos(Tt) =