Workshop #11 (Calculus III) - Edubirdie

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

2024
Views:

239

Pages:

1
Author:

accionox1v

Workshop #11 1. Find the length of the curve ~r(t) = h2et , e−t , 2ti, 0 ≤ t ≤ 1. 2. (a) Find the velocity, acceleration, and speed of the a particle with the position function ~r(t) = he2t , e−t i. (b) A portion of the graph of ~r(t) = he2t , e−t i is given below. Carefully sketch the position, velocity, and acceleration vectors at t = 0. 3. Find the velocity and position vectors of a particle that has the given acceleration and the specified initial velocity and position. (a) ~a(t) = ~i − ~j + 3~k, ~v (0) = 10~j, ~j(0) = ~0. (b) ~a(t) = 9 sin(3t)~i + cos(3t)~j +4~k, ~v(0) = 2~i − 7~k, ~r(0) = 3~i + 4~j. 4. Sketch the following regions in R2 . n o (a) R = (x, y) x2 + y 2 ≤ 9, and y ≥ −1 . n o (b) R = (x, y) x > 0, and x − y > 1 .

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