- 12.PE.1PE: In Exercises 1 and 2, graph the curves and sketch their velocity an...
- 12.PE.2PE: In Exercises 1 and 2, graph the curves and sketch their velocity an...
- 12.PE.3PE: The position of a particle in the plane at time t is Find the parti...
- 12.PE.4PE: Suppose Show that the angle between r and a never changes. What is ...
- 12.PE.6PE: Find the point on the curve where the curvature is greatest.
- 12.PE.5PE: Finding curvature At point P, the velocity and acceleration of a pa...
- 12.PE.7PE: A particle moves around the unit circle in the xy-plane. Its positi...
- 12.PE.8PE: You send a message through a pneumatic tube that follows the curve ...
- 12.PE.9PE: Characterizing circular motion A particle moves in the plane so tha...
- 12.PE.11PE: Shot put A shot leaves the thrower’s hand 6.5 ft above the ground a...
- 12.PE.10PE: Speed along a cycloid A circular wheel with radius 1 ft and center ...
- 12.PE.12PE: Javelin A javelin leaves the thrower’s hand 7 ft above the ground a...
- 12.PE.13PE: A golf ball is hit with an initial speed at an angle to the horizon...
- 12.PE.14PE: Javelin In Potsdam in 1988, Petra Felke of (then) East Germany set ...
- 12.PE.15PE: Find the lengths of the curves in Exercises 15 and 16.
- 12.PE.16PE: Find the lengths of the curves in Exercises 15 and 16.
- 12.PE.17PE: In Exercises 17–20, find T, N, B, k and at the given value of t.
- 12.PE.18PE: In Exercises 17–20, find T, N, B, k and at the given value of t.
- 12.PE.19PE: In Exercises 17–20, find T, N, B, k and at the given value of t.
- 12.PE.20PE: In Exercises 17–20, find T, N, B, k and at the given value of t.
- 12.PE.21PE: In Exercises 21 and 22, write a in the form at t = 0 without findin...
- 12.PE.22PE: In Exercises 21 and 22, write a in the form at t = 0 without findin...
- 12.PE.23PE: Find T, N, B, k and as functions of t if
- 12.PE.24PE: At what times in the interval are the velocity and acceleration vec...
- 12.PE.25PE: The position of a particle moving in space at time is Find the firs...
- 12.PE.26PE: Find equations for the osculating, normal, and rectifying planes of...
- 12.PE.27PE: Find parametric equations for the line that is tangent to the curve
- 12.PE.28PE: Find parametric equations for the line tangent to the helix r(t) = ...
- 12.PE.29PE: Synchronous curves By eliminating from the ideal projectile equatio...
- 12.PE.30PE: Radius of curvature Show that the radius of curvature of a twice-di...
- 12.PE.31PE: The view from Skylab 4 What percentage of Earth’s surface area coul...
- 12.PE.32PE: The position of a particle in the plane at time t is Find the parti...
Solutions for Chapter 12.PE: University Calculus: Early Transcendentals 2nd Edition
Full solutions for University Calculus: Early Transcendentals | 2nd Edition
Additive identity for the complex numbers
0 + 0i is the complex number zero
Angle between vectors
The angle formed by two nonzero vectors sharing a common initial point
Arc length formula
The length of an arc in a circle of radius r intercepted by a central angle of u radians is s = r u.
In an experiment with two possible outcomes, the probability of one outcome occurring k times in n independent trials is P1E2 = n!k!1n - k2!pk11 - p) n-k where p is the probability of the outcome occurring once
Characteristic polynomial of a square matrix A
det(xIn - A), where A is an n x n matrix
Difference of complex numbers
(a + bi) - (c + di) = (a - c) + (b - d)i
Equivalent equations (inequalities)
Equations (inequalities) that have the same solutions.
Identity involving a trigonometric function of u/2.
A graph that visually represents the information in a frequency table using rectangular areas proportional to the frequencies.
Hyperboloid of revolution
A surface generated by rotating a hyperbola about its transverse axis, p. 607.
Invertible linear system
A system of n linear equations in n variables whose coefficient matrix has a nonzero determinant.
A pair of real numbers (x, y), p. 12.
The various possible results of an experiment.
Quotient rule of logarithms
logb a R S b = logb R - logb S, R > 0, S > 0
The principle of experimental design that makes it possible to use the laws of probability when making inferences.
See Complex plane.
Real number line
A horizontal line that represents the set of real numbers.
Zeros of a function that are real numbers.
A positive number written as c x 10m, where 1 ? c < 10 and m is an integer.
Ratio change in y/change in x