1 Functions And Models 2 Limits And Derivatives 3 Differentiation Rules 4 Applications Of Differentiation 5 Integrals 6 Applications Of Integration 7 Techniques Of Integration 8 Further Applications Of Integration 9 Differential Equations 10 Parametric Equations And Polar Coordinates 11 Sequences, Series, And Power Series 12 Vectors And The Geometry Of Space 13 Vector Functions 14 Partial Derivatives 15 Multiple Integrals 16 Vector Calculus A Numbers, Inequalities, And Absolute Values B Coordinate Geometry And Lines C Graphs Of Second-degree Equations D Trigonometry E Sigma Notation F Proofs Of Theorems G The Logarithm Defined As An Integral expand_more
13.1 Vector Functions And Space Curves 13.2 Derivatives And Integrals Of Vector Functions 13.3 Arc Length And Curvature 13.4 Motion In Space: Velocity And Acceleration Chapter Questions expand_more
Problem 1CC Problem 2CC Problem 3CC Problem 4CC Problem 5CC Problem 6CC: (a) What is the definition of curvature? (b) Write a formula for curvature in terms of r'(t) and... Problem 7CC Problem 8CC Problem 9CC: State Keplers Laws. Problem 1TFQ Problem 2TFQ Problem 3TFQ Problem 4TFQ Problem 5TFQ Problem 6TFQ Problem 7TFQ Problem 8TFQ: Determine whether the statement is true or false. If it is true, explain why. If it is false,... Problem 9TFQ: Determine whether the statement is true or false. If it is true, explain why. If it is false,... Problem 10TFQ Problem 11TFQ Problem 12TFQ: Determine whether the statement is true or false. If it is true, explain why. If it is false,... Problem 13TFQ: Determine whether the statement is true or false. If it is true, explain why. If it is false,... Problem 14TFQ Problem 15TFQ Problem 16TFQ Problem 1E: (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 2E: 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 3E Problem 4E: Find parametric equations for the tangent line to the curve x = 2 sin t, y = 2 sin 2t, z = 2 sin 3t... Problem 5E: If r(t) = t2 i + t cos t j + sin t k, evaluate 01r(t) dt. Problem 6E Problem 7E Problem 8E Problem 9E: 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 10E Problem 11E: For the curve given by r(t) = sin3 t, cos3 t, sin2 t, 0 t /2, find (a) the unit tangent vector,... Problem 12E: Find the curvature of the ellipse x = 3 cos t, y = 4 sin t at the points (3, 0) and (0, 4). Problem 13E: Find the curvature of the curve y = x4 at the point (1, 1). Problem 14E: Find an equation of the osculating circle of the curve y = x4 x2 at the origin. Graph both the... Problem 15E: Find an equation of the osculating plane of the curve x = sin 2t, y = t, z = cos 2t at the point (0,... Problem 16E: The figure shows the curve C traced by a particle with position vector r(t) at time t. (a) Draw a... Problem 17E: A particle moves with position function r(t) = t ln t i + t j + et k. Find the velocity, speed, and... Problem 18E: Find the velocity, speed, and acceleration of a particle moving with position function r(t) = (2t2 ... Problem 19E: A particle starts at the origin with initial velocity i j + 3 k. Its acceleration is a(t) = 6t i +... Problem 20E: An athlete throws a shot at an angle of 45 to the horizontal at an initial speed of 43 ft/s. It... Problem 21E: A projectile is launched with an initial speed of 40 m/s from the floor of a tunnel whose height is... Problem 22E Problem 23E Problem 24E Problem 1PP: PROBLEM PLUS FIGURE FOR PROBLEM 1 1. A particle P moves with constant angular speed around a circle... Problem 2PP Problem 3PP: A projectile is fired from the origin with angle of elevation and initial speed v0. Assuming that... Problem 4PP: (a) A projectile it fired from the origin down an inclined plain: that makes an angle with the... Problem 5PP: 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 6PP: Find the curvature of the curve with parametric equations x=0tsin(122)d y=0tcos(122)d Problem 7PP: If a projectile is fired with angle of elevation and initial speed v. then parametric equations for... Problem 8PP: A cable has radius r and length L and is wound around a spool with radius R without over lapping.... Problem 9PP format_list_bulleted