MTH 232 WRITTEN ASSIGNMENT 3Answer all assigned exercises, and show all work. Each exercise is worth 5 points.
Please write answer neatly and clear as possible.If rewriting please write the question and section clearly.
Name: WA 3, p. 1 Name: University ID: Thomas Edison State University Calculus II (MAT-232) Section no.: Semester and year: Written Assignment 3 Answer all assigned exercises, and show all work. Each exercise is worth 5 points. Section 9.1 2. Sketch the plane curve defined by the given parametric equations, and find an x-y equation for the curve. {12cos 22sin xt yt =+ =-+ 8. Sketch the plane curve defined by the given parametric equations, and find an x-y equation for the curve. {2 2 1 1 xt yt =- =+ 12. Sketch the plane curve defined by the given parametric equations, and find an x-y equation for the curve. {2 t t xe ye - = = 22. Find parametric equations describing the given curve. The line segment from (3, 1) to (1, 3) 28. Find parametric equations describing the given curve. The circle of radius 5 centered at (–1, 3), counterclockwise Section 9.2 6. Find the slopes of the tangent lines to the given curves at the indicated points. {2 1 sin xt yt =+ = (a) t = –π (b) t = π (c) (0, 0) 8. Sketch the graph and find the slope of the curve at the given point. {3 42 54 xtt ytt =- =-+ at (0, 0) 20. Given the parametric equations for the position of an object, find the object’s velocity and speed at the given times and describe its motion. {3cossin3 3sincos3 xtt ytt =+ =+ (a) t = 0 (b) 2 t p = 26. Find the area enclosed by the given curve. {sin cos xtt ytt = = ,22 t pp -££ 28. Find the area enclosed by the given curve. {3 4 4 1 xtt yt =- =- ,22 t -££ Section 9.3 4. Find the arc length of each curve; compute one exactly and approximate the other numerically. (a) {cos sin xtt ytt = = ,11 t -££ (b) {2 2 cos sin xtt ytt = = , 11 t -££ 8. Find the arc length of each curve; compute one exactly and approximate the other numerically. (a) {2 4 4 xt yt = =+ , 12 t ££ (b) {3 362 3/ xt ytt =+ =+ , 12 t ££ 12. (a) Show that the curve starts at the origin at t = 0 and reaches the point (π, 2) at t = 1. (b) Use the time formula (3.2) to determine how long it would take a skier to take the given path. (c) Find the slope at the origin and the arc length for the curve. {0.6sin 20.4sin xtt ytt pp p =- =+ 16. Compute the surface area of the surface obtained by revolving the given curve about the indicated axis. {2 4 4 xt yt = =+ , 12 t ££ (a) about the x-axis(b) about x = 4 Section 9.4 2. Plot the given polar points (r, θ) and find their rectangular representation. (2,) p 8. Find all polar coordinate representations of the given rectangular point. (–1, 1) 12. Find all polar coordinate representations of the given rectangular point. (2,5) -- 14. Find rectangular coordinates for the given polar point. 3 (1,) p - 22. Sketch and describe the graph of the polar equation and find a corresponding x-y equation. 3/4 qp = 26. Sketch and describe the graph of the polar equation and find a corresponding x-y equation. 2sin r q =