Problem 1RCC Problem 2RCC Problem 3RCC Problem 4RCC Problem 5RCC Problem 6RCC: (a) What is the definition of curvature? (b) Write a formula for curvature in terms of r'(t) and... Problem 7RCC Problem 8RCC Problem 9RCC: State Keplers Laws. Problem 1RQ Problem 2RQ Problem 3RQ Problem 4RQ Problem 5RQ Problem 6RQ Problem 7RQ Problem 8RQ: Determine whether the statement is true or false. If it is true, explain why. If it is false,... Problem 9RQ: Determine whether the statement is true or false. If it is true, explain why. If it is false,... Problem 10RQ Problem 11RQ Problem 12RQ: Determine whether the statement is true or false. If it is true, explain why. If it is false,... Problem 13RQ: Determine whether the statement is true or false. If it is true, explain why. If it is false,... Problem 14RQ Problem 1RE: (a) Sketch the curve with vector function r(t) = t i + cos t j + sin t k t 0 (b) Find r'(t) and... Problem 2RE: Let r(t) = 2-t, (et 1)/t, ln(t + 1). (a) Find the domain of r. (b) Find limt0 r(t). (c) Find r'(t). Problem 3RE Problem 4RE: Find parametric equations for the tangent line to the curve x = 2 sin t, y = 2 sin 2t, z = 2 sin 3t... Problem 5RE: If r(t) = t2 i + t cos t j + sin t k, evaluate 01r(t) dt. Problem 6RE Problem 7RE Problem 8RE Problem 9RE: The helix r1(t) = cos t i + sin t j + t k intersects the curve r2(t) = (1 + t)i + t2 j + t3 k at the... Problem 10RE Problem 11RE: For the curve given by r(t) = sin3 t, cos3 t, sin2 t, 0 t /2, find (a) the unit tangent vector,... Problem 12RE: Find the curvature of the ellipse x = 3 cos t, y = 4 sin t at the points (3, 0) and (0, 4). Problem 13RE: Find the curvature of the curve y = x4 at the point (1, 1). Problem 14RE: Find an equation of the osculating circle of the curve y = x4 x2 at the origin. Graph both the... Problem 15RE: Find an equation of the osculating plane of the curve x = sin 2t, y = t, z = cos 2t at the point (0,... Problem 16RE: The figure shows the curve C traced by a particle with position vector r(t) at time t. (a) Draw a... Problem 17RE: A particle moves with position function r(t) = t ln t i + t j + et k. Find the velocity, speed, and... Problem 18RE: Find the velocity, speed, and acceleration of a particle moving with position function r(t) = (2t2 ... Problem 19RE: A particle starts at the origin with initial velocity i j + 3 k. Its acceleration is a(t) = 6t i +... Problem 20RE: An athlete throws a shot at an angle of 45 to the horizontal at an initial speed of 43 ft/s. It... Problem 21RE: A projectile is launched with an initial speed of 40 m/s from the floor of a tunnel whose height is... Problem 22RE Problem 23RE Problem 1P: PROBLEM PLUS FIGURE FOR PROBLEM 1 1. A particle P moves with constant angular speed around a circle... Problem 2P: A circular curve of radius R on a highway is banked at an angle so that a car can safely traverse... Problem 3P: A projectile is fired from the origin with angle of elevation and initial speed v0. Assuming that... Problem 4P: (a) A projectile it fired from the origin down an inclined plain: that makes an angle with the... Problem 5P: A ball rolls off a table with a speed of 2 ft/s. The table is 3.5 ft high. (a) Determine the point... Problem 6P: Find the curvature of the curve with parametric equations x=0tsin(122)d y=0tcos(122)d Problem 7P: If a projectile is fired with angle of elevation and initial speed v. then parametric equations for... Problem 8P: A cable has radius r and length L and is wound around a spool with radius R without over lapping.... Problem 9P format_list_bulleted