Name: College ID: Thomas Edison State College 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. { x 1 2cos t y 2 2sin t 8. Sketch the plane curve defined by the given parametric equations, and find an x-y equation for the curve. { x t 2 1 y t2 1 12. Sketch the plane curve defined by the given parametric equations, and find an x-y equation for the curve. WA 3, p. 1 { x et y e 2 t 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. { (a) t = -(b) t = (c) (0, 0) x t 1 y sin t 2 8. Sketch the graph and find the slope of the curve at the given point. { x t3 t y t 4 5t 2 4 WA 3, p. 2 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. { x 3cos t sin 3t y 3sin t cos 3t (a) t = 0(b) t 2 26. Find the area enclosed by the given curve. { x t sin t y t cos t , t 2 2 28. Find the area enclosed by the given curve. { x t 3 4t , 2 t 2 y t 4 1 Section 9.3 4. Find the arc length of each curve; compute one exactly and approximate the other numerically. WA 3, p. 3 (a) (b) { { , x t cos t 1 t 1 y t sin t , x t 2 cos t 1 t 1 y t 2 sin t 8. Find the arc length of each curve; compute one exactly and approximate the other numerically. (a) { x 4t , 1 t 2 y t2 4 (b) { x 36t 2 , 1 t 2 y t3 3 / t 12. (a) Show that the curve starts at the origin at t = 0 and reaches the point (, 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. WA 3, p. 4 { x t 0.6sin t y 2t 0.4sin t 16. Compute the surface area of the surface obtained by revolving the given curve about the indicated axis. { x 4t , 1 t 2 (a) about the x-axis (b) about x = 4 y t2 4 Section 9.4 2. Plot the given polar points (r, ) and find their rectangular representation. (2, ) 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) WA 3, p. 5 14. Find rectangular coordinates for the given polar point. (1, ) 3 22. Sketch and describe the graph of the polar equation and find a corresponding x-y equation. 3 / 4 26. Sketch and describe the graph of the polar equation and find a corresponding x-y equation. r 2sin WA 3, p. 6 \f