University:
Seattle Pacific University
Course:
MAT 1236 | Calculus III
Academic year:

2024
Views:

123

Pages:

1
Author:

ddifenwadbyx

Workshop #8 1. Sketch the part of the circle given by the parameterization. Be sure to denote direction, as well as the initial and terminal points. 3π 7π ≤t≤ 4 4 π 3π (b) ~r = hcos(2t), sin(2t)i, ≤t≤ 2 2 D t t E π 3π (c) ~r = cos , sin , ≤t≤ 2 2 2 2 D√ t + 7, ln(9 − t), 2. Find the domain of ~r = (a) ~r = hcos(t), sin(t)i, 1 E and sketch it on a number line. 3t − 6 3. Show that the curve with parametric equations x = 4 sin t, y = 4 cos t, z = sin2 t lies on the intersection of 16z = x2 and x2 + y 2 = 16. 4. Do the following paths intersect? Do particles traveling along the paths collide? Find any points of intersection, or collision points. (a) ~q = 5t~i + (t − 3)~j + (t2 + 1) ~k ~r = t2 ~i + (2t − 8)~j + (4t + 6) ~k (b) ~q = (t + 4)~i + (2t + 1)~j + t2 ~k ~r = 3t~i + (7 − t)~j + t3 ~k