University:
Georgia Southern University
Course:
MATH 2243 | Calculus 3
Academic year:

2024
Views:

156

Pages:

1
Author:

Jalen W.

Instructor: Shijun Zheng Course: Spring 2023 - Calculus III (MATH2243-A-B) Student: Jalen Wilson Date: 07/11/24 Assignment: Sec. 13.3 Enhanced Assign 1. Find thecurve's unit tangent vector.Also, find the length of the indicated portion of the curve. 0≤t≤π r(t) = (7cos t)i + (7sin t)j + ( 7 t)k, Find thecurve's unit tangent vector. T(t) = − 7 14 28 sin t i + 7 14 2 14 π The length of the curve is 98 cos t j + 28 k 28 . (Type an exactanswer, using π asneeded.) YOUANSWERED: 2 7 π 2. Find thecurve's unit tangent vector.Also, find the length of the indicated portion of the curve. 2 r(t) = ti + 3 t 3/2 k, 0 ≤ t ≤ 8 1 Thecurve's unit tangent vector is i + 1+t 0 j+ t 1+t k. (Type exactanswers, using radicals asneeded.) 52 The length of the indicated portion of the curve is 3 units. (Type an integer or a simplifiedfraction.) 3. Find thecurve's unit tangent vector.Also, find the length of the indicated portion of the curve. 3 3 r(t) = 7 cos t j + 7 sin t k, 0≤t≤ π 4 Find thecurve's unit tangent vector. T(t) = − cos t j+ sin t k 21 The length of the curve is . 4 (Type an exactanswer, using π asneeded.) t 4. Find the arc length parameter along the curve from the point where t = 0 by evaluating the integral s = ∫ |v|dτ. Then find the length of the 0 indicated portion of the curve. t t t r(t) = 3e cos t i + 3e sin t j + 3e k, − ln 4 ≤ t ≤ 0 t The arc length parameter is s(t) = 3 3 e − 1 . (Type an exactanswer, using radicals as needed.) The length of the indicated portion of the curve is (Type an exactanswer, using radicals as needed.) 9 3 4 units.