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

2024
Views:

400

Pages:

2
Author:

Jalen W.

Instructor: Shijun Zheng Course: Spring 2023 - Calculus III (MATH2243-A-B) Student: Jalen Wilson Date: 07/11/24 Assignment: Sect 13.1 Enhanced Assign 1. Find the limit or indicate that it does not exist. lim t →π sin 5 3 t i+ cos t 4 j+ tan 11 6 t k Select the correct choice belowand, ifnecessary, fill in the answer box in your choice. A. 3 5 t 11 lim sin t i + cos j + tan t k = − 3 4 6 2 t →π (Type an exactanswer, using π and radicals asneeded.) 2 i+ j+ 2 − 3 3 k B. The limit does not exist and is not ∞ or − ∞. 2 2. The position of a particle in thexy-plane at time t is r(t) = (t + 4) i + t − 3 j. Find an equation in x and y whose graph is the path of the particle. Then find theparticle's velocity and acceleration vectors at t = 3. The equation for the path of the particle is y = The velocity vector at t = 3 is v = ( (Simplify youranswers.) 1 . ) i + ( The acceleration vector at t = 3 is a = ( (Simplify youranswers.) 3. 2 (x − 4) − 3 0 6 ) j. ) i + ( 2 ) j. 7 2t e j. Find an equation in x and y whose graph is the path of the 25 particle. Then find theparticle's velocity and acceleration vectors at t = ln 5. The position of a particle in thexy-plane at time t is r(t) = e 7 2 x The equation for the path of the particle is y = The velocity vector at t = ln 5 is v = ( (Simplify youranswers.) i+ . 25 5 The acceleration vector at t = ln 5 is a = ( (Simplify youranswers.) t ) i + ( 5 14 ) i + ( ) j. 28 ) j. 4. The path r(t) = (t − sin t) i + (1 − cos t) j describes motion on the cycloid x = t − sin t, y = 1 − cos t. Find theparticle's velocity and acceleration vectors at t = π, and sketch them as vectors on the curve. The velocity vector at t = π is v(π) = 2 i+ 0 j. (Simplify youranswer, including any radicals. Use integers or fractions for any numbers in the expression.) The acceleration vector at t = π is a(π) = 0 i+ −1 j. (Simplify youranswer, including any radicals. Use integers or fractions for any numbers in the expression.) Choose the correct sketch for theparticle's velocity and acceleration at t = π. A. B. y C. y a D. y a y v v v v x x a x a x 5. The path r(t) = (t) i + t2 + 6 j describes motion on the parabola y = x2 + 6. Find theparticle's velocity and acceleration vectors at t = − 3, and sketch them as vectors on the curve. The velocity vector at t = − 3 is v( − 3) = 1 i+ −6 j. (Simplify youranswer, including any radicals. Use integers or fractions for any numbers in the expression.) The acceleration vector at t = − 3 is a( − 3) = 0 i+ 2 j. (Simplify youranswer, including any radicals. Use integers or fractions for any numbers in the expression.) Choose the correct sketch for theparticle's velocity and acceleration at t = − 3. A. B. C. y y a y v a x x v v x a 6. The vector function r(t) is the position of a particle in space at time t. Determine the graph of the position function. r(t) = (3t cos t)i + (t sin t)j + 2tk Choose the correct graph below. A. B. C. D.