Consider the curve r (t) = (sin³ (t), cos³ (t), sin² (t)) for 0 ≤ t≤ π/2. Compute the following quantities at the point t = π/4. The unit normal vector N (4) = (−, −, −). (a component in first answer box, y component in second answer box, z component in third) The unit binormal vector B (4) = (−, —, —). (a component in first answer box, y component in second answer box, z component in third) The curvature (1)

Calc 3

Find Components of the Acceleration For the curve defined by 7(t) = (e-t cos(t), eʻ sin(t)) find the unit tangent vector, unit normal vector, normal acceleration, and tangential acceleration at t = 3 T(플) - N(플) - 3 3 AN =

(8) Subtracting the two equations, find a vector equation for the curve of 3 intersection between y= 4x² +=' and y-1=3x += for x > 0. Find 4 1 and simplify the tangential component of acceleration for your curve. 3 2 cos (2t) + cos 2t a sin? t- sin? (2r) –4 cos?t 3 2sin? (21) - sin 21 Vsin' - sin? t- sin? (2t) –4cos?t 2sin (21)- sin 21 3 sin? t + sin? (21) +4cos?t 3 2 sin (21) +sin 21 /sin?t + sin? (21) + 4 cos²t