Question

(1 pt) (a) On a separate sheet of paper, sketch the parameterized curvextcost, y = sint for OSIS 4x. Use your graph to complete the following statement: Att = 2.5, a particle moving along the curve in the direction of increasing I is moving down and to the left (6) By calculating the position at i = 2.5 and 1 = 2.51, estimate the speed at t = 2.5. speed (c) Use derivatives to calculate the speed at 1 = 2.5 and compare your answer to part (b). speed

Answer 1

The graph of the curves x = cos(t),y=tsin(t): x=t.cos(t) 110 5 2 6 8 10 12 10 =tsin() The particle moving along the curve in the direction of increasing t is moving down and to the left. a. Speed:

r(t) = (x(t),y(t)) = {tcost,t sint) r(2.5)=(2.5 cos (2.5), 2.5 sin (2.5)) (2.51) = (2.51 cos(2.51),2.51sin (2.51) (2.51)--(2.5)|= V(2.51 cos(2.51)- 2.5 cos(2.51)| +(2.5cos(2.5)-2.5cos(2.5)) = 0.026972 Speed: |(2.51) –> (2.5) P(2.5)= 2.51-2.5 0.026972 0.01 = 2.6972 Derivatives are, r' (t)=(x'(t),y'(t)) = (cost-tsint,-sint-t cost) 7' (2.5)= (cos(2.5) – 2.5 sin (2.5).-sin (2.5) – 2.5 cos(2.5)) || p (2.5) = (cos(2.5) – 2.5 sin (2.5))* +(-sin(2.5)-2.5 cos(2.5)) = 2.6926